using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.Globalization;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using System.Text;

namespace YukiCoder
{
	class Program
	{
		static void Main()
		{
			using var cin = new Scanner();
			int n = cin.Int();
			var (m, k) = cin.Long2();

			var nums = new long[n];
			long mm = m;
			for (int i = 0; i < n; i++) {
				nums[i] = i;
				mm -= i;
			}

			long div = mm / n;
			long rem = mm % n;
			for (int i = 0; i < n; i++) {
				nums[i] += div;
				if (i >= n - rem) {
					nums[i] += 1;
				}
			}

			nums = nums.OrderBy(i => Guid.NewGuid()).ToArray();

			var set = new RedBlackTree<long>(nums);
			var ans = new long[n];
			for (int i = n - 1; i >= 0; i--) {
				if (k > 0 && k >= i) {
					ans[i] = set[set.Count - 1 - i];
					set.Remove(ans[i]);
					k -= i;
				} else {
					ans[i] = set.Max;
					set.RemoveAt(set.Count - 1);
				}
			}

			Console.WriteLine(ans.JoinNL());
		}
	}

	public class RedBlackTree<T> : ICollection<T>, IReadOnlyCollection<T>
		where T : IComparable<T>
	{
		private readonly bool isMulti_;
		private readonly Stack<Node> pool_ = new Stack<Node>();
		private Node root_;

		public RedBlackTree(bool isMulti = false)
		{
			isMulti_ = isMulti;
		}

		public RedBlackTree(IEnumerable<T> collection, bool isMulti = false)
		{
			isMulti_ = isMulti;
			var arr = InitializeArray(collection);
			root_ = ConstructRootFromSortedArray(arr, 0, arr.Length - 1, null);
		}

		public T this[int index] => Find(index);

		public int Count => CountOf(root_);
		public T Min
		{
			get
			{
				if (root_ is null) {
					return default;
				}

				var cur = root_;
				while (cur.Left is null == false) {
					cur = cur.Left;
				}

				return cur.Item;
			}
		}

		public T Max
		{
			get
			{
				if (root_ is null) {
					return default;
				}

				var cur = root_;
				while (cur.Right is null == false) {
					cur = cur.Right;
				}

				return cur.Item;
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public bool Contains(T item) => FindNode(item) is null == false;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public int IndexOf(T item) => Index(FindNode(item));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public T Find(int index)
		{
			var node = FindNodeByIndex(index);
			return node is null == false ? node.Item : default;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public void Add(T item)
		{
			if (root_ is null) {
				root_ = NewNode(item, false);
				return;
			}

			Node current = root_;
			Node parent = null;
			Node grandParent = null;
			Node greatGrandParent = null;
			int order = 0;
			while (current is null == false) {
				order = item.CompareTo(current.Item);
				if (order == 0 && isMulti_ == false) {
					root_.IsRed = false;
					return;
				}

				if (current.Is4Node()) {
					current.Split4Node();
					if (Node.IsNonNullRed(parent) == true) {
						InsertionBalance(current, ref parent, grandParent, greatGrandParent);
					}
				}

				greatGrandParent = grandParent;
				grandParent = parent;
				parent = current;
				current = (order < 0) ? current.Left : current.Right;
			}

			Node node = NewNode(item, true);
			if (order >= 0) {
				parent.Right = node;
			} else {
				parent.Left = node;
			}

			if (parent.IsRed) {
				InsertionBalance(node, ref parent, grandParent, greatGrandParent);
			}

			root_.IsRed = false;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public bool RemoveAt(int index) => Remove(FindNodeByIndex(index).Item);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public bool Remove(T item)
		{
			if (root_ is null) {
				return false;
			}

			Node current = root_;
			Node parent = null;
			Node grandParent = null;
			Node match = null;
			Node parentOfMatch = null;
			bool foundMatch = false;
			while (current is null == false) {
				if (current.Is2Node()) {
					if (parent is null) {
						current.IsRed = true;
					} else {
						Node sibling = parent.GetSibling(current);
						if (sibling.IsRed) {
							if (parent.Right == sibling) {
								parent.RotateLeft();
							} else {
								parent.RotateRight();
							}

							parent.IsRed = true;
							sibling.IsRed = false;
							ReplaceChildOrRoot(grandParent, parent, sibling);
							grandParent = sibling;
							if (parent == match) {
								parentOfMatch = sibling;
							}

							sibling = (parent.Left == current) ? parent.Right : parent.Left;
						}

						if (sibling.Is2Node()) {
							parent.Merge2Nodes();
						} else {
							TreeRotation rotation = parent.GetRotation(current, sibling);
							Node newGrandParent = parent.Rotate(rotation);
							newGrandParent.IsRed = parent.IsRed;
							parent.IsRed = false;
							current.IsRed = true;
							ReplaceChildOrRoot(grandParent, parent, newGrandParent);
							if (parent == match) {
								parentOfMatch = newGrandParent;
							}
						}
					}
				}

				int order = foundMatch ? -1 : item.CompareTo(current.Item);
				if (order == 0) {
					foundMatch = true;
					match = current;
					parentOfMatch = parent;
				}

				grandParent = parent;
				parent = current;
				current = order < 0 ? current.Left : current.Right;
			}

			if (match is null == false) {
				ReplaceNode(match, parentOfMatch, parent, grandParent);
				match.Clear();
				pool_.Push(match);
			}

			if (root_ is null == false) {
				root_.IsRed = false;
			}

			return foundMatch;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public void Clear()
		{
			root_ = null;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public void CopyTo(T[] array, int arrayIndex)
		{
			foreach (var item in this) {
				array[arrayIndex++] = item;
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (int index, T value) Prev((int index, T value) node)
			=> (node.index - 1, Find(node.index - 1));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (int index, T value) Next((int index, T value) node)
			=> (node.index + 1, Find(node.index + 1));

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (int index, T value) LowerBound(T item) => BinarySearch(item, true);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (int index, T value) UpperBound(T item) => BinarySearch(item, false);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (int index, T value) BinarySearch(T item, bool isLowerBound)
		{
			Node right = null;
			int ri = -1;
			Node current = root_;
			if (current is null) {
				return (ri, default);
			}

			ri = 0;
			while (current is null == false) {
				var order = item.CompareTo(current.Item);
				if (order < 0 || (isLowerBound && order == 0)) {
					right = current;
					current = current.Left;
				} else {
					ri += CountOf(current.Left) + 1;
					current = current.Right;
				}
			}

			return right is null == false ? (ri, right.Item) : (ri, default);
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		private static int CountOf(Node node) => node is null ? 0 : node.Size;

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		private Node NewNode(T item, bool isRed)
		{
			if (pool_.Count > 0) {
				var node = pool_.Pop();
				node.Item = item;
				node.IsRed = isRed;
				return node;
			} else {
				return new Node(item, isRed);
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		private Node FindNode(T item)
		{
			Node current = root_;
			while (current is null == false) {
				int cmp = item.CompareTo(current.Item);
				if (cmp == 0) {
					return current;
				}

				current = cmp < 0 ? current.Left : current.Right;
			}

			return null;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		private int Index(Node node)
		{
			if (node is null) {
				return -1;
			}

			var ret = CountOf(node.Left);
			Node prev = node;
			node = node.Parent;
			while (prev != root_) {
				if (node.Left != prev) {
					ret += CountOf(node.Left) + 1;
				}

				prev = node;
				node = node.Parent;
			}

			return ret;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		private Node FindNodeByIndex(int index)
		{
			var current = root_;
			var currentIndex = current.Size - CountOf(current.Right) - 1;
			while (currentIndex != index) {
				if (currentIndex > index) {
					current = current.Left;
					if (current is null) {
						break;
					}

					currentIndex -= CountOf(current.Right) + 1;
				} else {
					current = current.Right;
					if (current is null) {
						break;
					}

					currentIndex += CountOf(current.Left) + 1;
				}
			}

			return current;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		private T[] InitializeArray(IEnumerable<T> collection)
		{
			T[] array;
			if (isMulti_) {
				array = collection.ToArray();
				Array.Sort(array, (x, y) => x.CompareTo(y));
			} else {
				var list = new List<T>(collection);
				list.Sort((x, y) => x.CompareTo(y));
				for (int i = list.Count - 1; i > 0; i--) {
					if (list[i - 1].CompareTo(list[i]) == 0) {
						list.RemoveAt(i);
					}
				}

				array = list.ToArray();
			}

			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		private Node ConstructRootFromSortedArray(T[] arr, int startIndex, int endIndex, Node redNode)
		{
			int size = endIndex - startIndex + 1;
			Node root;
			switch (size) {
				case 0:
					return null;

				case 1:
					root = NewNode(arr[startIndex], false);
					if (redNode is null == false) {
						root.Left = redNode;
					}

					break;

				case 2:
					root = NewNode(arr[startIndex], false);
					root.Right = NewNode(arr[endIndex], true);
					if (redNode is null == false) {
						root.Left = redNode;
					}

					break;

				case 3:
					root = NewNode(arr[startIndex + 1], false);
					root.Left = NewNode(arr[startIndex], false);
					root.Right = NewNode(arr[endIndex], false);
					if (redNode is null == false) {
						root.Left.Left = redNode;
					}

					break;

				default:
					int midpt = ((startIndex + endIndex) / 2);
					root = NewNode(arr[midpt], false);
					root.Left = ConstructRootFromSortedArray(arr, startIndex, midpt - 1, redNode);
					root.Right = size % 2 == 0
						? ConstructRootFromSortedArray(arr, midpt + 2, endIndex, NewNode(arr[midpt + 1], true))
						: ConstructRootFromSortedArray(arr, midpt + 1, endIndex, null);

					break;
			}

			return root;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		private void ReplaceNode(Node match, Node parentOfMatch, Node succesor, Node parentOfSuccesor)
		{
			if (succesor == match) {
				succesor = match.Left;
			} else {
				if (succesor.Right is null == false) {
					succesor.Right.IsRed = false;
				}

				if (parentOfSuccesor != match) {
					parentOfSuccesor.Left = succesor.Right;
					succesor.Right = match.Right;
				}

				succesor.Left = match.Left;
			}

			if (succesor is null == false) {
				succesor.IsRed = match.IsRed;
			}

			ReplaceChildOrRoot(parentOfMatch, match, succesor);
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		private void InsertionBalance(Node current, ref Node parent, Node grandParent, Node greatGrandParent)
		{
			bool parentIsOnRight = grandParent.Right == parent;
			bool currentIsOnRight = parent.Right == current;
			Node newChildOfGreatGrandParent;
			if (parentIsOnRight == currentIsOnRight) {
				newChildOfGreatGrandParent = currentIsOnRight
					? grandParent.RotateLeft()
					: grandParent.RotateRight();
			} else {
				newChildOfGreatGrandParent = currentIsOnRight
					? grandParent.RotateLeftRight()
					: grandParent.RotateRightLeft();
				parent = greatGrandParent;
			}

			grandParent.IsRed = true;
			newChildOfGreatGrandParent.IsRed = false;
			ReplaceChildOrRoot(greatGrandParent, grandParent, newChildOfGreatGrandParent);
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		private void ReplaceChildOrRoot(Node parent, Node child, Node newChild)
		{
			if (parent is null == false) {
				if (parent.Left == child) {
					parent.Left = newChild;
				} else {
					parent.Right = newChild;
				}
			} else {
				root_ = newChild;
			}
		}

		bool ICollection<T>.IsReadOnly => false;
		public IEnumerable<T> Reverse()
		{
			var e = new Enumerator(this, true);
			while (e.MoveNext()) {
				yield return e.Current;
			}
		}

		public Enumerator GetEnumerator() => new Enumerator(this);
		IEnumerator<T> IEnumerable<T>.GetEnumerator() => new Enumerator(this);
		System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() => new Enumerator(this);

		private class Node
		{
			public bool IsRed { get; set; }
			public T Item { get; set; }
			public Node Parent { get; private set; }

			private Node _Left;
			public Node Left
			{
				get => _Left;
				set
				{
					_Left = value;
					Update(value);
				}
			}

			private Node _Right;
			public Node Right
			{
				get => _Right;
				set
				{
					_Right = value;
					Update(value);
				}
			}
			public int Size { get; private set; } = 1;
			public Node(T item, bool isRed)
			{
				Item = item;
				IsRed = isRed;
			}

			[MethodImpl(MethodImplOptions.AggressiveInlining)]
			public void Clear()
			{
				Parent = null;
				_Left = null;
				_Right = null;
				Size = 1;
			}

			[MethodImpl(MethodImplOptions.AggressiveInlining)]
			public void Update(Node child)
			{
				if (child is null == false) {
					child.Parent = this;
				}

				for (var cur = this; cur is null == false; cur = cur.Parent) {
					if (!cur.UpdateSize()) {
						break;
					}

					if (cur.Parent is null == false
						&& cur.Parent.Left != cur
						&& cur.Parent.Right != cur) {
						cur.Parent = null;
						return;
					}
				}
			}

			[MethodImpl(MethodImplOptions.AggressiveInlining)]
			public bool UpdateSize()
			{
				var oldsize = Size;
				var size = 1;
				if (Left is null == false) {
					size += Left.Size;
				}
				if (Right is null == false) {
					size += Right.Size;
				}

				Size = size;
				return oldsize != size;
			}

			[MethodImpl(MethodImplOptions.AggressiveInlining)]
			public static bool IsNonNullRed(Node node) => node is null == false && node.IsRed;
			[MethodImpl(MethodImplOptions.AggressiveInlining)]
			public static bool IsNonNullBlack(Node node) => node is null == false && node.IsRed == false;
			[MethodImpl(MethodImplOptions.AggressiveInlining)]
			public static bool IsNullOrBlack(Node node) => node is null || node.IsRed == false;

			[MethodImpl(MethodImplOptions.AggressiveInlining)]
			public bool Is2Node() => IsRed == false && IsNullOrBlack(Left) && IsNullOrBlack(Right);
			[MethodImpl(MethodImplOptions.AggressiveInlining)]
			public bool Is4Node() => IsNonNullRed(Left) && IsNonNullRed(Right);

			[MethodImpl(MethodImplOptions.AggressiveInlining)]
			public void Merge2Nodes()
			{
				IsRed = false;
				Left.IsRed = true;
				Right.IsRed = true;
			}

			[MethodImpl(MethodImplOptions.AggressiveInlining)]
			public void Split4Node()
			{
				IsRed = true;
				Left.IsRed = false;
				Right.IsRed = false;
			}

			[MethodImpl(MethodImplOptions.AggressiveInlining)]
			public TreeRotation GetRotation(Node current, Node sibling)
			{
				if (IsNonNullRed(sibling.Left)) {
					if (Left == current) {
						return TreeRotation.RightLeft;
					}

					return TreeRotation.Right;
				} else {
					if (Left == current) {
						return TreeRotation.Left;
					}

					return TreeRotation.LeftRight;
				}
			}

			[MethodImpl(MethodImplOptions.AggressiveInlining)]
			public Node GetSibling(Node node)
			{
				return Left == node ? Right : Left;
			}

			[MethodImpl(MethodImplOptions.AggressiveInlining)]
			public Node Rotate(TreeRotation rotation)
			{
				switch (rotation) {
					default:
					case TreeRotation.Right:
						Left.Left.IsRed = false;
						return RotateRight();

					case TreeRotation.Left:
						Right.Right.IsRed = false;
						return RotateLeft();

					case TreeRotation.RightLeft:
						return RotateRightLeft();

					case TreeRotation.LeftRight:
						return RotateLeftRight();
				}
			}

			[MethodImpl(MethodImplOptions.AggressiveInlining)]
			public Node RotateLeft()
			{
				Node child = Right;
				Right = child.Left;
				child.Left = this;
				return child;
			}

			[MethodImpl(MethodImplOptions.AggressiveInlining)]
			public Node RotateLeftRight()
			{
				Node child = Left;
				Node grandChild = child.Right;
				Left = grandChild.Right;
				grandChild.Right = this;
				child.Right = grandChild.Left;
				grandChild.Left = child;
				return grandChild;
			}

			[MethodImpl(MethodImplOptions.AggressiveInlining)]
			public Node RotateRight()
			{
				Node child = Left;
				Left = child.Right;
				child.Right = this;
				return child;
			}

			[MethodImpl(MethodImplOptions.AggressiveInlining)]
			public Node RotateRightLeft()
			{
				Node child = Right;
				Node grandChild = child.Left;
				Right = grandChild.Left;
				grandChild.Left = this;
				child.Left = grandChild.Right;
				grandChild.Right = child;
				return grandChild;
			}

			public override string ToString() => $"size = {Size}, item = {Item}";
		}

		public enum TreeRotation : byte
		{
			Left = 1,
			Right = 2,
			RightLeft = 3,
			LeftRight = 4,
		}

		public struct Enumerator : IEnumerator<T>
		{
			private readonly RedBlackTree<T> tree_;
			private readonly Stack<Node> stack_;
			private readonly bool reverse_;
			private Node current_;

			internal Enumerator(RedBlackTree<T> tree, bool reverse = false)
			{
				tree_ = tree;
				stack_ = new Stack<Node>(2 * Log2(tree_.Count + 1));
				current_ = null;
				reverse_ = reverse;
				Intialize(tree_.root_);
			}

			private void Intialize(Node startNode)
			{
				current_ = null;
				Node node = startNode;
				Node next;
				while (node != null) {
					next = (reverse_ ? node.Right : node.Left);
					stack_.Push(node);
					node = next;
				}
			}

			[MethodImpl(MethodImplOptions.AggressiveInlining)]
			private static int Log2(int num) => num == 0 ? 0 : BitOperations.Log2((uint)num) + 1;
			object System.Collections.IEnumerator.Current => Current;
			public T Current => current_ is null ? default : current_.Item;
			[MethodImpl(MethodImplOptions.AggressiveInlining)]
			public bool MoveNext()
			{
				if (stack_.Count == 0) {
					current_ = null;
					return false;
				}

				current_ = stack_.Pop();
				var node = reverse_ ? current_.Left : current_.Right;
				Node next;
				while (node is null == false) {
					next = reverse_ ? node.Right : node.Left;
					stack_.Push(node);
					node = next;
				}

				return true;
			}

			[MethodImpl(MethodImplOptions.AggressiveInlining)]
			public void Reset() => throw new NotSupportedException();

			public void Dispose() { }
		}
	}

	public struct BitFlag
	{
		public static BitFlag Begin() => 0;
		public static BitFlag End(int bitCount) => 1 << bitCount;
		public static BitFlag FromBit(int bitNumber) => 1 << bitNumber;
		public static BitFlag Fill(int count) => (1 << count) - 1;

		private readonly int flags_;
		public int Flag => flags_;
		public bool this[int bitNumber] => (flags_ & (1 << bitNumber)) != 0;
		public BitFlag(int flags) { flags_ = flags; }

		public bool Has(BitFlag target) => (flags_ & target.flags_) == target.flags_;
		public bool Has(int target) => (flags_ & target) == target;
		public bool HasBit(int bitNumber) => (flags_ & (1 << bitNumber)) != 0;
		public BitFlag OrBit(int bitNumber) => (flags_ | (1 << bitNumber));
		public BitFlag AndBit(int bitNumber) => (flags_ & (1 << bitNumber));
		public BitFlag XorBit(int bitNumber) => (flags_ ^ (1 << bitNumber));
		public BitFlag ComplementOf(BitFlag sub) => flags_ ^ sub.flags_;
		public int PopCount() => BitOperations.PopCount((uint)flags_);

		public static BitFlag operator ++(BitFlag src) => new BitFlag(src.flags_ + 1);
		public static BitFlag operator --(BitFlag src) => new BitFlag(src.flags_ - 1);
		public static BitFlag operator |(BitFlag lhs, BitFlag rhs)
			=> new BitFlag(lhs.flags_ | rhs.flags_);
		public static BitFlag operator |(BitFlag lhs, int rhs)
			=> new BitFlag(lhs.flags_ | rhs);
		public static BitFlag operator |(int lhs, BitFlag rhs)
			=> new BitFlag(lhs | rhs.flags_);
		public static BitFlag operator &(BitFlag lhs, BitFlag rhs)
			=> new BitFlag(lhs.flags_ & rhs.flags_);
		public static BitFlag operator &(BitFlag lhs, int rhs)
			=> new BitFlag(lhs.flags_ & rhs);
		public static BitFlag operator &(int lhs, BitFlag rhs)
			=> new BitFlag(lhs & rhs.flags_);

		public static bool operator <(BitFlag lhs, BitFlag rhs) => lhs.flags_ < rhs.flags_;
		public static bool operator <(BitFlag lhs, int rhs) => lhs.flags_ < rhs;
		public static bool operator <(int lhs, BitFlag rhs) => lhs < rhs.flags_;
		public static bool operator >(BitFlag lhs, BitFlag rhs) => lhs.flags_ > rhs.flags_;
		public static bool operator >(BitFlag lhs, int rhs) => lhs.flags_ > rhs;
		public static bool operator >(int lhs, BitFlag rhs) => lhs > rhs.flags_;
		public static bool operator <=(BitFlag lhs, BitFlag rhs) => lhs.flags_ <= rhs.flags_;
		public static bool operator <=(BitFlag lhs, int rhs) => lhs.flags_ <= rhs;
		public static bool operator <=(int lhs, BitFlag rhs) => lhs <= rhs.flags_;
		public static bool operator >=(BitFlag lhs, BitFlag rhs) => lhs.flags_ >= rhs.flags_;
		public static bool operator >=(BitFlag lhs, int rhs) => lhs.flags_ >= rhs;
		public static bool operator >=(int lhs, BitFlag rhs) => lhs >= rhs.flags_;

		public static implicit operator BitFlag(int t) => new BitFlag(t);
		public static implicit operator int(BitFlag t) => t.flags_;

		public override string ToString() => $"{Convert.ToString(flags_, 2).PadLeft(32, '0')} ({flags_})";

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public void ForEachSubBits(Action<BitFlag> action)
		{
			for (BitFlag sub = (flags_ - 1) & flags_; sub > 0; sub = --sub & flags_) {
				action(sub);
			}
		}

		public SubBitsEnumerator SubBits => new SubBitsEnumerator(flags_);
		public struct SubBitsEnumerator : IEnumerable<BitFlag>
		{
			private readonly int flags_;
			public SubBitsEnumerator(int flags)
			{
				flags_ = flags;
			}

			IEnumerator<BitFlag> IEnumerable<BitFlag>.GetEnumerator() => new Enumerator(flags_);
			IEnumerator IEnumerable.GetEnumerator() => new Enumerator(flags_);
			public Enumerator GetEnumerator() => new Enumerator(flags_);
			public struct Enumerator : IEnumerator<BitFlag>
			{
				private readonly int src_;
				public BitFlag Current { get; private set; }
				object IEnumerator.Current => Current;

				public Enumerator(int flags)
				{
					src_ = flags;
					Current = flags;
				}

				public void Dispose() { }
				[MethodImpl(MethodImplOptions.AggressiveInlining)]
				public bool MoveNext() => (Current = --Current & src_) > 0;
				[MethodImpl(MethodImplOptions.AggressiveInlining)]
				public void Reset() => Current = src_;
			}
		}
	}

	public class HashMap<TKey, TValue> : Dictionary<TKey, TValue>
	{
		private readonly Func<TKey, TValue> initialzier_;
		public HashMap(Func<TKey, TValue> initialzier)
			: base()
		{
			initialzier_ = initialzier;
		}

		public HashMap(Func<TKey, TValue> initialzier, int capacity)
			: base(capacity)
		{
			initialzier_ = initialzier;
		}

		new public TValue this[TKey key]
		{
			get
			{
				if (TryGetValue(key, out TValue value)) {
					return value;
				} else {
					var init = initialzier_(key);
					base[key] = init;
					return init;
				}
			}

			set { base[key] = value; }
		}

		public HashMap<TKey, TValue> Merge(
			HashMap<TKey, TValue> src,
			Func<TValue, TValue, TValue> mergeValues)
		{
			foreach (var key in src.Keys) {
				this[key] = mergeValues(this[key], src[key]);
			}

			return this;
		}
	}

	public class JagList2<T> where T : struct
	{
		private readonly int n_;
		private readonly List<T>[] tempValues_;
		private T[][] values_;

		public int Count => n_;
		public List<T>[] Raw => tempValues_;
		public T[][] Values => values_;
		public T[] this[int index] => values_[index];

		public JagList2(int n)
		{
			n_ = n;
			tempValues_ = new List<T>[n];
			for (int i = 0; i < n; ++i) {
				tempValues_[i] = new List<T>();
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public void Add(int i, T value) => tempValues_[i].Add(value);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public void Build()
		{
			values_ = new T[n_][];
			for (int i = 0; i < values_.Length; ++i) {
				values_[i] = tempValues_[i].ToArray();
			}
		}
	}

	public class DijkstraQ
	{
		private int count_ = 0;
		private long[] distanceHeap_;
		private int[] vertexHeap_;

		public int Count => count_;
		public DijkstraQ()
		{
			distanceHeap_ = new long[8];
			vertexHeap_ = new int[8];
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public void Enqueue(long distance, int v)
		{
			if (distanceHeap_.Length == count_) {
				var newDistanceHeap = new long[distanceHeap_.Length << 1];
				var newVertexHeap = new int[vertexHeap_.Length << 1];
				Unsafe.CopyBlock(
					ref Unsafe.As<long, byte>(ref newDistanceHeap[0]),
					ref Unsafe.As<long, byte>(ref distanceHeap_[0]),
					(uint)(8 * count_));
				Unsafe.CopyBlock(
					ref Unsafe.As<int, byte>(ref newVertexHeap[0]),
					ref Unsafe.As<int, byte>(ref vertexHeap_[0]),
					(uint)(4 * count_));
				distanceHeap_ = newDistanceHeap;
				vertexHeap_ = newVertexHeap;
			}

			ref var dRef = ref distanceHeap_[0];
			ref var vRef = ref vertexHeap_[0];
			Unsafe.Add(ref dRef, count_) = distance;
			Unsafe.Add(ref vRef, count_) = v;
			++count_;

			int c = count_ - 1;
			while (c > 0) {
				int p = (c - 1) >> 1;
				var tempD = Unsafe.Add(ref dRef, p);
				if (tempD <= distance) {
					break;
				} else {
					Unsafe.Add(ref dRef, c) = tempD;
					Unsafe.Add(ref vRef, c) = Unsafe.Add(ref vRef, p);
					c = p;
				}
			}

			Unsafe.Add(ref dRef, c) = distance;
			Unsafe.Add(ref vRef, c) = v;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (long distance, int v) Dequeue()
		{
			ref var dRef = ref distanceHeap_[0];
			ref var vRef = ref vertexHeap_[0];
			(long distance, int v) ret = (dRef, vRef);
			int n = count_ - 1;

			var distance = Unsafe.Add(ref dRef, n);
			var vertex = Unsafe.Add(ref vRef, n);
			int p = 0;
			int c = (p << 1) + 1;
			while (c < n) {
				if (c != n - 1 && Unsafe.Add(ref dRef, c + 1) < Unsafe.Add(ref dRef, c)) {
					++c;
				}

				var tempD = Unsafe.Add(ref dRef, c);
				if (distance > tempD) {
					Unsafe.Add(ref dRef, p) = tempD;
					Unsafe.Add(ref vRef, p) = Unsafe.Add(ref vRef, c);
					p = c;
					c = (p << 1) + 1;
				} else {
					break;
				}
			}

			Unsafe.Add(ref dRef, p) = distance;
			Unsafe.Add(ref vRef, p) = vertex;
			--count_;

			return ret;
		}
	}

	public struct ModInt
	{
		//public const long P = 1000000007;
		public const long P = 998244353;
		//public const long P = 10;
		public const long ROOT = 3;

		// (924844033, 5)
		// (998244353, 3)
		// (1012924417, 5)
		// (167772161, 3)
		// (469762049, 3)
		// (1224736769, 3)

		private long value_;

		public static ModInt New(long value, bool mods) => new ModInt(value, mods);
		public ModInt(long value) => value_ = value;
		public ModInt(long value, bool mods)
		{
			if (mods) {
				value %= P;
				if (value < 0) {
					value += P;
				}
			}

			value_ = value;
		}

		public static ModInt operator +(ModInt lhs, ModInt rhs)
		{
			lhs.value_ = (lhs.value_ + rhs.value_) % P;
			return lhs;
		}
		public static ModInt operator +(long lhs, ModInt rhs)
		{
			rhs.value_ = (lhs + rhs.value_) % P;
			return rhs;
		}
		public static ModInt operator +(ModInt lhs, long rhs)
		{
			lhs.value_ = (lhs.value_ + rhs) % P;
			return lhs;
		}

		public static ModInt operator -(ModInt lhs, ModInt rhs)
		{
			lhs.value_ = (P + lhs.value_ - rhs.value_) % P;
			return lhs;
		}
		public static ModInt operator -(long lhs, ModInt rhs)
		{
			rhs.value_ = (P + lhs - rhs.value_) % P;
			return rhs;
		}
		public static ModInt operator -(ModInt lhs, long rhs)
		{
			lhs.value_ = (P + lhs.value_ - rhs) % P;
			return lhs;
		}

		public static ModInt operator *(ModInt lhs, ModInt rhs)
		{
			lhs.value_ = lhs.value_ * rhs.value_ % P;
			return lhs;
		}
		public static ModInt operator *(long lhs, ModInt rhs)
		{
			rhs.value_ = lhs * rhs.value_ % P;
			return rhs;
		}
		public static ModInt operator *(ModInt lhs, long rhs)
		{
			lhs.value_ = lhs.value_ * rhs % P;
			return lhs;
		}

		public static ModInt operator /(ModInt lhs, ModInt rhs)
			=> lhs * Inverse(rhs);

		public static implicit operator ModInt(long n) => new ModInt(n, true);

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static ModInt Inverse(ModInt value) => Pow(value, P - 2);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static ModInt Pow(ModInt value, long k) => Pow(value.value_, k);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static ModInt Pow(long value, long k)
		{
			long ret = 1;
			while (k > 0) {
				if ((k & 1) != 0) {
					ret = ret * value % P;
				}

				value = value * value % P;
				k >>= 1;
			}

			return new ModInt(ret);
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public long ToLong() => value_;
		public override string ToString() => value_.ToString();
	}

	public static class Helper
	{
		public static long INF => 1L << 60;

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T Clamp<T>(this T value, T min, T max) where T : struct, IComparable<T>
		{
			if (value.CompareTo(min) <= 0) {
				return min;
			}

			if (value.CompareTo(max) >= 0) {
				return max;
			}

			return value;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void UpdateMin<T>(this ref T target, T value) where T : struct, IComparable<T>
			=> target = target.CompareTo(value) > 0 ? value : target;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void UpdateMin<T>(this ref T target, T value, Action<T> onUpdated)
			where T : struct, IComparable<T>
		{
			if (target.CompareTo(value) > 0) {
				target = value;
				onUpdated(value);
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void UpdateMax<T>(this ref T target, T value) where T : struct, IComparable<T>
			=> target = target.CompareTo(value) < 0 ? value : target;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void UpdateMax<T>(this ref T target, T value, Action<T> onUpdated)
			where T : struct, IComparable<T>
		{
			if (target.CompareTo(value) < 0) {
				target = value;
				onUpdated(value);
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[] Array1<T>(int n, T initialValue) where T : struct
			=> new T[n].Fill(initialValue);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[] Array1<T>(int n, Func<int, T> initializer)
			=> Enumerable.Range(0, n).Select(x => initializer(x)).ToArray();
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[] Fill<T>(this T[] array, T value)
			where T : struct
		{
			array.AsSpan().Fill(value);
			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[,] Array2<T>(int n, int m, T initialValule) where T : struct
			=> new T[n, m].Fill(initialValule);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[,] Array2<T>(int n, int m, Func<int, int, T> initializer)
		{
			var array = new T[n, m];
			for (int i = 0; i < n; ++i) {
				for (int j = 0; j < m; ++j) {
					array[i, j] = initializer(i, j);
				}
			}

			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[,] Fill<T>(this T[,] array, T initialValue)
			where T : struct
		{
			MemoryMarshal.CreateSpan<T>(ref array[0, 0], array.Length).Fill(initialValue);
			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static Span<T> AsSpan<T>(this T[,] array, int i)
			=> MemoryMarshal.CreateSpan<T>(ref array[i, 0], array.GetLength(1));

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[,,] Array3<T>(int n1, int n2, int n3, T initialValue)
			where T : struct
			=> new T[n1, n2, n3].Fill(initialValue);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[,,] Fill<T>(this T[,,] array, T initialValue)
			where T : struct
		{
			MemoryMarshal.CreateSpan<T>(ref array[0, 0, 0], array.Length).Fill(initialValue);
			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static Span<T> AsSpan<T>(this T[,,] array, int i, int j)
			=> MemoryMarshal.CreateSpan<T>(ref array[i, j, 0], array.GetLength(2));

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[,,,] Array4<T>(int n1, int n2, int n3, int n4, T initialValue)
			where T : struct
			=> new T[n1, n2, n3, n4].Fill(initialValue);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[,,,] Fill<T>(this T[,,,] array, T initialValue)
			where T : struct
		{
			MemoryMarshal.CreateSpan<T>(ref array[0, 0, 0, 0], array.Length).Fill(initialValue);
			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static Span<T> AsSpan<T>(this T[,,,] array, int i, int j, int k)
			=> MemoryMarshal.CreateSpan<T>(ref array[i, j, k, 0], array.GetLength(3));

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[] Merge<T>(ReadOnlySpan<T> first, ReadOnlySpan<T> second) where T : IComparable<T>
		{
			var ret = new T[first.Length + second.Length];
			int p = 0;
			int q = 0;
			while (p < first.Length || q < second.Length) {
				if (p == first.Length) {
					ret[p + q] = second[q];
					q++;
					continue;
				}

				if (q == second.Length) {
					ret[p + q] = first[p];
					p++;
					continue;
				}

				if (first[p].CompareTo(second[q]) < 0) {
					ret[p + q] = first[p];
					p++;
				} else {
					ret[p + q] = second[q];
					q++;
				}
			}

			return ret;
		}

		private static readonly int[] delta4_ = { 1, 0, -1, 0, 1 };
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void DoIn4(int i, int j, int imax, int jmax, Action<int, int> action)
		{
			for (int dn = 0; dn < 4; ++dn) {
				int d4i = i + delta4_[dn];
				int d4j = j + delta4_[dn + 1];
				if ((uint)d4i < (uint)imax && (uint)d4j < (uint)jmax) {
					action(d4i, d4j);
				}
			}
		}

		private static readonly int[] delta8_ = { 1, 0, -1, 0, 1, 1, -1, -1, 1 };
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void DoIn8(int i, int j, int imax, int jmax, Action<int, int> action)
		{
			for (int dn = 0; dn < 8; ++dn) {
				int d8i = i + delta8_[dn];
				int d8j = j + delta8_[dn + 1];
				if ((uint)d8i < (uint)imax && (uint)d8j < (uint)jmax) {
					action(d8i, d8j);
				}
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void ForEachSubBits(int bit, Action<int> action)
		{
			for (int sub = bit; sub >= 0; --sub) {
				sub &= bit;
				action(sub);
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static string Reverse(string src)
		{
			var chars = src.ToCharArray();
			for (int i = 0, j = chars.Length - 1; i < j; ++i, --j) {
				var tmp = chars[i];
				chars[i] = chars[j];
				chars[j] = tmp;
			}

			return new string(chars);
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void Swap(this string str, int i, int j)
		{
			var span = str.AsWriteableSpan();
			(span[i], span[j]) = (span[j], span[i]);
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static char Replace(this string str, int index, char c)
		{
			var span = str.AsWriteableSpan();
			char old = span[index];
			span[index] = c;
			return old;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static Span<char> AsWriteableSpan(this string str)
		{
			var span = str.AsSpan();
			return MemoryMarshal.CreateSpan(ref MemoryMarshal.GetReference(span), span.Length);
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static string Join<T>(this IEnumerable<T> values, string separator = "")
			=> string.Join(separator, values);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static string JoinNL<T>(this IEnumerable<T> values)
			=> string.Join(Environment.NewLine, values);
	}

	public static class Extensions
	{
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static Span<T> AsSpan<T>(this List<T> list)
		{
			return Unsafe.As<FakeList<T>>(list).Array.AsSpan(0, list.Count);
		}

		private class FakeList<T>
		{
			public T[] Array = null;
		}
	}

	public class Scanner : IDisposable
	{
		private const int BUFFER_SIZE = 1024;
		private const int ASCII_CHAR_BEGIN = 33;
		private const int ASCII_CHAR_END = 126;
		private readonly string filePath_;
		private readonly Stream stream_;
		private readonly byte[] buf_ = new byte[BUFFER_SIZE];
		private int length_ = 0;
		private int index_ = 0;
		private bool isEof_ = false;

		public Scanner(string file = "")
		{
			if (string.IsNullOrWhiteSpace(file)) {
				stream_ = Console.OpenStandardInput();
			} else {
				filePath_ = file;
				stream_ = new FileStream(file, FileMode.Open);
			}

			Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) {
				AutoFlush = false
			});
		}

		public void Dispose()
		{
			Console.Out.Flush();
			stream_.Dispose();
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public char Char()
		{
			byte b;
			do {
				b = Read();
			} while (b < ASCII_CHAR_BEGIN || ASCII_CHAR_END < b);

			return (char)b;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public string Next()
		{
			var sb = new StringBuilder();
			for (var b = Char(); b >= ASCII_CHAR_BEGIN && b <= ASCII_CHAR_END; b = (char)Read()) {
				sb.Append(b);
			}

			return sb.ToString();
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public string[] ArrayString(int length)
		{
			var array = new string[length];
			for (int i = 0; i < length; ++i) {
				array[i] = Next();
			}

			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public int Int() => (int)Long();
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public int Int(int offset) => Int() + offset;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (int, int) Int2(int offset = 0)
			=> (Int(offset), Int(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (int, int, int) Int3(int offset = 0)
			=> (Int(offset), Int(offset), Int(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (int, int, int, int) Int4(int offset = 0)
			=> (Int(offset), Int(offset), Int(offset), Int(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public int[] ArrayInt(int length, int offset = 0)
		{
			var array = new int[length];
			for (int i = 0; i < length; ++i) {
				array[i] = Int(offset);
			}

			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public long Long()
		{
			long ret = 0;
			byte b;
			bool ng = false;
			do {
				b = Read();
			} while (b != '-' && (b < '0' || '9' < b));

			if (b == '-') {
				ng = true;
				b = Read();
			}

			for (; true; b = Read()) {
				if (b < '0' || '9' < b) {
					return ng ? -ret : ret;
				} else {
					ret = ret * 10 + b - '0';
				}
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public long Long(long offset) => Long() + offset;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (long, long) Long2(long offset = 0)
			=> (Long(offset), Long(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (long, long, long) Long3(long offset = 0)
			=> (Long(offset), Long(offset), Long(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (long, long, long, long) Long4(long offset = 0)
			=> (Long(offset), Long(offset), Long(offset), Long(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public long[] ArrayLong(int length, long offset = 0)
		{
			var array = new long[length];
			for (int i = 0; i < length; ++i) {
				array[i] = Long(offset);
			}

			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public BigInteger Big() => new BigInteger(Long());
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public BigInteger Big(long offset) => Big() + offset;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (BigInteger, BigInteger) Big2(long offset = 0)
			=> (Big(offset), Big(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (BigInteger, BigInteger, BigInteger) Big3(long offset = 0)
			=> (Big(offset), Big(offset), Big(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (BigInteger, BigInteger, BigInteger, BigInteger) Big4(long offset = 0)
			=> (Big(offset), Big(offset), Big(offset), Big(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public BigInteger[] ArrayBig(int length, long offset = 0)
		{
			var array = new BigInteger[length];
			for (int i = 0; i < length; ++i) {
				array[i] = Big(offset);
			}

			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public double Double() => double.Parse(Next(), CultureInfo.InvariantCulture);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public double Double(double offset) => Double() + offset;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (double, double) Double2(double offset = 0)
			=> (Double(offset), Double(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (double, double, double) Double3(double offset = 0)
			=> (Double(offset), Double(offset), Double(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (double, double, double, double) Double4(double offset = 0)
			=> (Double(offset), Double(offset), Double(offset), Double(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public double[] ArrayDouble(int length, double offset = 0)
		{
			var array = new double[length];
			for (int i = 0; i < length; ++i) {
				array[i] = Double(offset);
			}

			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public decimal Decimal() => decimal.Parse(Next(), CultureInfo.InvariantCulture);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public decimal Decimal(decimal offset) => Decimal() + offset;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (decimal, decimal) Decimal2(decimal offset = 0)
			=> (Decimal(offset), Decimal(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (decimal, decimal, decimal) Decimal3(decimal offset = 0)
			=> (Decimal(offset), Decimal(offset), Decimal(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (decimal, decimal, decimal, decimal) Decimal4(decimal offset = 0)
			=> (Decimal(offset), Decimal(offset), Decimal(offset), Decimal(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public decimal[] ArrayDecimal(int length, decimal offset = 0)
		{
			var array = new decimal[length];
			for (int i = 0; i < length; ++i) {
				array[i] = Decimal(offset);
			}

			return array;
		}

		private byte Read()
		{
			if (isEof_) {
				throw new EndOfStreamException();
			}

			if (index_ >= length_) {
				index_ = 0;
				if ((length_ = stream_.Read(buf_, 0, BUFFER_SIZE)) <= 0) {
					isEof_ = true;
					return 0;
				}
			}

			return buf_[index_++];
		}

		public void Save(string text)
		{
			if (string.IsNullOrWhiteSpace(filePath_)) {
				return;
			}

			File.WriteAllText(filePath_ + "_output.txt", text);
		}
	}
}