using Lib;
using Lib.GraphLib;
using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Runtime.CompilerServices;
using System.Text;
using static Lib.OutputLib;
public class Solver
{
    const bool MultiTestCase = false;
    void Solve()
    {
        int n = ri;

        var seg = new Seg(n);
        for (int i = 0; i < n - 1; i++) seg.AddEdge(ri - 1, ri - 1);
        seg.Build();
        var a = new int[n];

        int q = ri;
        while (q-- > 0)
        {
            if (ri == 1)
            {
                int x = ri - 1;
                seg.Set(x, a[x] ^= 1);
            }
            else
            {
                int x = ri - 1;
                int l = -1, r = n;
                while (r - l > 1)
                {
                    int m = (l + r) / 2;
                    if (seg.Prod(x, m + 1) == 0) l = m;
                    else r = m;
                }
                Write(r);
            }
        }
    }

    /// <summary>
    /// 木および可換モノイドについて次のクエリを O(n(logn)^2) で処理.
    /// - 一点更新 : ある頂点に書かれた値を変更.
    /// - 範囲取得 : ある頂点から距離 l 以上 r 未満の頂点についての総和.
    /// <see cref="https://judge.yosupo.jp/problem/vertex_add_range_contour_sum_on_tree"/>
    /// </summary>
    public class Seg
    {
        public readonly int Size;
        SegTree<int, IntAddGroup>[] seg;
        (int i, int j)[][] seg_idx;
        int[][] depth_idx;
        int[] left, right, parent, root;
        UnweightedGraph g;
        LowestCommonAncestor lca;
        int[] csr, csr_start, depth;
        int[] data;
        public Seg(int n)
        {
            Size = n;
            g = new UnweightedGraph(n);
            data = new int[n];
            Array.Fill(data, 0);
        }
        public void AddEdge(int u, int v) => g.AddEdge(u, v);
        public void Build()
        {
            (csr, csr_start) = g.ToCSR();
            var cd = new CentroidDecomposition(g);
            var rev_ord = cd.GetReversedOrderSpan();
            var in_time = cd.GetInTimeSpan();

            var cd_children = new List<int>[Size];
            for (int i = 0; i < Size; i++) cd_children[i] = new List<int>();
            var cd_parent = cd.GetParentSpan();
            for (int i = 0; i < Size; i++) if (cd_parent[i] != -1) cd_children[cd_parent[i]].Add(i);
            int dummy_count = 0;
            for (int x = 0; x < Size; x++)
            {
                int cnt = 0;
                var es = csr.AsSpan(csr_start[x], csr_start[x + 1] - csr_start[x]);
                foreach (var y in es) if (in_time[x] < in_time[y]) cnt++;
                dummy_count += Math.Max(0, cnt - 1);
            }

            int size_all = Size + dummy_count;
            var weight = new int[size_all];
            seg = new SegTree<int, IntAddGroup>[Size + size_all];
            var seg_idx_list = new List<(int i, int j)>[Size];
            for (int i = 0; i < seg_idx_list.Length; i++) seg_idx_list[i] = new List<(int, int)>();
            depth_idx = new int[Size + size_all][];

            left = new int[size_all]; Array.Fill(left, -1);
            right = new int[size_all]; Array.Fill(right, -1);
            parent = new int[size_all]; Array.Fill(parent, -1);
            root = new int[size_all];

            var qu = new Queue<(int x, int p)>();
            var pq = new PriorityQueue<int, int>();
            int dummy_idx = Size;
            var dist = new int[Size];
            var vs_buf = new (int x, int d)[size_all][];

            lca = new LowestCommonAncestor(g, rev_ord[^1]);
            depth = new int[Size];
            qu.Enqueue((rev_ord[^1], -1));
            while (qu.Count > 0)
            {
                var (x, p) = qu.Dequeue();
                var es = csr.AsSpan(csr_start[x], csr_start[x + 1] - csr_start[x]);
                foreach (var y in es) if (y != p) { depth[y] = depth[x] + 1; qu.Enqueue((y, x)); }
            }

            foreach (var r in rev_ord)
            {
                var vs_list = new List<(int x, int d)>();
                dist[r] = 0;
                qu.Enqueue((r, -1));
                while (qu.Count > 0)
                {
                    var (x, p) = qu.Dequeue();
                    vs_list.Add((x, dist[x]));
                    var es = csr.AsSpan(csr_start[x], csr_start[x + 1] - csr_start[x]);
                    foreach (var y in es)
                    {
                        if (in_time[r] > in_time[y] || y == p) continue;
                        dist[y] = dist[x] + 1;
                        qu.Enqueue((y, x));
                    }
                }
                {
                    weight[r] = vs_list.Count;
                    depth_idx[r] = new int[vs_list[^1].d + 2];
                    var data = new int[vs_list.Count];
                    for (int i = 0, j = 0; i < vs_list.Count; i++)
                    {
                        var (x, d) = vs_list[i];
                        data[i] = this.data[x];
                        while (j <= d) depth_idx[r][j++] = i;
                        seg_idx_list[x].Add((r, i));
                    }
                    depth_idx[r][^1] = vs_list.Count;
                    seg[r] = new SegTree<int, IntAddGroup>(data);
                }

                var real_children = csr.AsSpan(csr_start[r], csr_start[r + 1] - csr_start[r]);
                foreach (var s in real_children)
                {
                    if (in_time[s] < in_time[r]) continue;
                    vs_list = new List<(int x, int d)>();
                    qu.Enqueue((s, r));
                    dist[s] = 1;
                    int cd_child = -1;
                    while (qu.Count > 0)
                    {
                        var (x, p) = qu.Dequeue();
                        vs_list.Add((x, dist[x]));
                        if (cd_parent[x] == r) cd_child = x;
                        var es = csr.AsSpan(csr_start[x], csr_start[x + 1] - csr_start[x]);
                        foreach (var y in es)
                        {
                            if (in_time[r] > in_time[y] || y == p) continue;
                            dist[y] = dist[x] + 1;
                            qu.Enqueue((y, x));
                        }
                    }
                    var vs = vs_list.ToArray();
                    int idx = Size + cd_child;
                    depth_idx[idx] = new int[vs[^1].d + 2];
                    var data = new int[vs.Length];
                    for (int i = 0, j = 0; i < vs.Length; i++)
                    {
                        var (x, d) = vs[i];
                        data[i] = this.data[x];
                        while (j <= d) depth_idx[idx][j++] = i;
                        seg_idx_list[x].Add((idx, i));
                    }
                    depth_idx[idx][^1] = vs.Length;
                    seg[idx] = new SegTree<int, IntAddGroup>(data);
                    root[cd_child] = r;
                    vs_buf[cd_child] = vs;
                    pq.Enqueue(cd_child, weight[cd_child]);
                }

                if (pq.Count > 0)
                {
                    while (pq.Count >= 2)
                    {
                        int u = pq.Dequeue();
                        int v = pq.Dequeue();
                        weight[dummy_idx] = weight[u] + weight[v];
                        left[parent[u] = dummy_idx] = u;
                        right[parent[v] = dummy_idx] = v;
                        pq.Enqueue(dummy_idx, weight[dummy_idx]);

                        var vs = new (int x, int d)[vs_buf[u].Length + vs_buf[v].Length];
                        {
                            int i = 0, j = 0, k = 0;
                            for (; i < vs_buf[u].Length && j < vs_buf[v].Length;)
                                vs[k++] = vs_buf[u][i].d <= vs_buf[v][j].d ? vs_buf[u][i++] : vs_buf[v][j++];
                            vs_buf[u].AsSpan(i).CopyTo(vs.AsSpan(k));
                            k += vs_buf[u].Length - i;
                            vs_buf[v].AsSpan(j).CopyTo(vs.AsSpan(k));
                        }

                        root[dummy_idx] = r;
                        int idx = Size + dummy_idx;
                        depth_idx[idx] = new int[vs[^1].d + 2];
                        var data = new int[vs.Length];
                        for (int i = 0, j = 0; i < vs.Length; i++)
                        {
                            var (x, d) = vs[i];
                            data[i] = this.data[x];
                            while (j <= d) depth_idx[idx][j++] = i;
                            seg_idx_list[x].Add((idx, i));
                        }
                        depth_idx[idx][^1] = vs.Length;
                        seg[idx] = new SegTree<int, IntAddGroup>(data);
                        vs_buf[dummy_idx++] = vs;
                    }
                    parent[left[r] = pq.Dequeue()] = r;
                }
            }

            seg_idx = new (int i, int j)[Size][];
            for (int i = 0; i < seg_idx.Length; i++) seg_idx[i] = seg_idx_list[i].ToArray();
        }
        public int Get(int x) => data[x];
        [MethodImpl(256)]
        public void Set(int x, int v)
        {
            data[x] = v;
            foreach (var (i, j) in seg_idx[x]) seg[i].Set(j, v);
        }
        [MethodImpl(256)]
        public void Apply(int x, int v)
        {
            data[x] += v;
            foreach (var (i, j) in seg_idx[x]) seg[i].Apply(j, v);
        }
        [MethodImpl(256)]
        public int Prod(int x, int r)
        {
            int x0 = x;
            int ret = InnerProd(x, r);
            while (parent[x] != -1)
            {
                int y = left[parent[x]] != x ? left[parent[x]] : right[parent[x]];
                if (y != -1)
                {
                    int d = depth[x0] + depth[root[y]] - 2 * depth[lca.LCA(x0, root[y])];
                    ret += InnerProd(y + Size, r - d);
                }
                x = parent[x];
                if (x != -1 && x < Size)
                {
                    int d = depth[x0] + depth[x] - 2 * depth[lca.LCA(x0, x)];
                    if (d < r) ret += data[x];
                }
            }
            return ret;
        }
        [MethodImpl(256)]
        private int InnerProd(int x, int r)
        {
            int d = depth_idx[x].Length - 1;
            if (r > d) r = d;
            return 0 < r ? seg[x].Prod(depth_idx[x][0], depth_idx[x][r]) : 0;
        }
    }


#pragma warning disable CS0162, CS8618
    public Solver() { if (!MultiTestCase) Solve(); else for (int t = ri; t > 0; t--) Solve(); }
#pragma warning restore CS0162, CS8618

    const int IINF = 1 << 30;
    const long INF = 1L << 60;
    int ri { [MethodImpl(256)] get => (int)sc.Integer(); }
    long rl { [MethodImpl(256)] get => sc.Integer(); }
    uint rui { [MethodImpl(256)] get => (uint)sc.UInteger(); }
    ulong rul { [MethodImpl(256)] get => sc.UInteger(); }
    double rd { [MethodImpl(256)] get => sc.Double(); }
    string rs { [MethodImpl(256)] get => sc.Scan(); }
    string rline { [MethodImpl(256)] get => sc.Line(); }
    public StreamScanner sc = new StreamScanner(Console.OpenStandardInput());
    void ReadArray(out int[] a, int n) { a = new int[n]; for (int i = 0; i < a.Length; i++) a[i] = ri; }
    void ReadArray(out long[] a, int n) { a = new long[n]; for (int i = 0; i < a.Length; i++) a[i] = rl; }
    void ReadArray<T>(out T[] a, int n, Func<T> read) { a = new T[n]; for (int i = 0; i < a.Length; i++) a[i] = read(); }
    void ReadArray<T>(out T[] a, int n, Func<int, T> read) { a = new T[n]; for (int i = 0; i < a.Length; i++) a[i] = read(i); }
}

static class Program
{
    static public void Main(string[] args)
    {
        SourceExpander.Expander.Expand();
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        new Solver();
        Console.Out.Flush();
    }
}
#region Expanded by https://github.com/kzrnm/SourceExpander
namespace Lib{public class SegTree<T,Op>where Op:struct,IMonoid<T>{private static readonly Op op=default;public int Length{get;}protected readonly int log,size;public readonly T[]d;public SegTree(int sz){Length=sz;log=0;while((1<<log)<Length)log++;size=1<<log;d=new T[2*size];Array.Fill(d,op.Identity);}public SegTree(T[]v):this(v.Length){for(int i=0;i<Length;i++)d[size+i]=v[i];for(int i=size-1;i>0;i--)Update(i);}[MethodImpl(256)]public void Clear()=>Array.Fill(d,op.Identity);[MethodImpl(256)]internal void SetWithoutUpdate(int p,T v)=>d[p+size]=v;[MethodImpl(256)]internal void AllUpdate(){for(int i=size-1;i>0;i--)Update(i);}[MethodImpl(256)]private void Update(int p)=>d[p]=op.Operate(d[2*p],d[2*p+1]);[MethodImpl(256)]public T Get(int p)=>d[p+size];[MethodImpl(256)]public void Set(int p,T v){p+=size;d[p]=v;for(int i=1;i<=log;i++)Update(p>>i);}[MethodImpl(256)]public void Apply(int p,T v){p+=size;d[p]=op.Operate(d[p],v);for(int i=1;i<=log;i++)Update(p>>i);}public T AllProd()=>d[1];[MethodImpl(256)]public T Prod(int l,int r){T sl=op.Identity,sr=op.Identity;l+=size;r+=size;while(l<r){if((l&1)!=0)sl=op.Operate(sl,d[l++]);if((r&1)!=0)sr=op.Operate(d[ --r],sr);l>>=1;r>>=1;}return op.Operate(sl,sr);}[MethodImpl(256)]public int MaxRight(int l,Predicate<T>f){if(l==Length)return Length;l+=size;var s=op.Identity;do{while(l%2==0)l>>=1;if(!f(op.Operate(s,d[l]))){while(l<size){l<<=1;if(f(op.Operate(s,d[l]))){s=op.Operate(s,d[l]);l++;}}return l-size;}s=op.Operate(s,d[l]);l++;}while((l&-l)!=l);return Length;}[MethodImpl(256)]public int MinLeft(int r,Predicate<T>f){if(r==0)return 0;r+=size;var s=op.Identity;do{r--;while(r>1&&(r%2)!=0)r>>=1;if(!f(op.Operate(d[r],s))){while(r<size){r=(2*r+1);if(f(op.Operate(d[r],s))){s=op.Operate(d[r],s);r--;}}return r+1-size;}s=op.Operate(d[r],s);}while((r&-r)!=r);return 0;}}}
public class SimpleIntStack{int[]data;int index;public SimpleIntStack(int size_max){data=new int[size_max];index=0;}public int Count{get=>index;}public void Push(int value)=>data[index++]=value;public int Peek()=>data[index-1];public int Pop()=>data[ --index];public void Clear()=>index=0;}public class SimpleIntPairStack{(int,int)[]data;int index;public SimpleIntPairStack(int size_max){data=new(int,int)[size_max];index=0;}public int Count{get=>index;}public void Push((int,int)value)=>data[index++]=value;public void Push(int item1,int item2)=>data[index++]=(item1,item2);public(int,int)Peek()=>data[index-1];public(int,int)Pop()=>data[ --index];public void Clear()=>index=0;}
public class SparseTable<T>{public int Length{get;}readonly T[][]st;Func<T,T,T>op;public SparseTable(ReadOnlySpan<T>arr,Func<T,T,T>_op){Length=arr.Length;op=_op;int log=1;while((Length>>log)>0)log++;st=new T[log][];st[0]=arr.ToArray();for(int k=1;k<st.Length;k++){var stp=st[k-1];var sti=st[k]=new T[Length-(1<<k)+1];for(int i=0;i<sti.Length;i++)sti[i]=op(stp[i],stp[i+(1<<(k-1))]);}}public T this[Range r]{[MethodImpl(256)]get{int j=0;while((1<<j)<=r.End.Value-r.Start.Value)j++;j--;return op(st[j][r.Start.Value],st[j][r.End.Value-(1<<j)]);}}public T Prod(int l,int r){int j=0;while((1<<j)<=r-l)j++;j--;return op(st[j][l],st[j][r-(1<<j)]);}}
namespace Lib{public class Graph<T>{public struct Edge{public int from,to;public T data;public Edge(int _from,int _to,T _data){from=_from;to=_to;data=_data;}public Edge(int _to,T _data){from=-1;to=_to;data=_data;}}int n;public int Size=>n;public List<Edge>[]edges;public Graph(Graph<T>_g){n=_g.Size;edges=new List<Edge>[n];for(int i=0;i<n;i++)edges[i]=new List<Edge>(_g.edges[i]);}public Graph(List<int>[]_g,Func<T>_e){n=_g.Length;edges=new List<Edge>[n];for(int i=0;i<n;i++)edges[i]=new List<Edge>();for(int i=0;i<n;i++)foreach(var j in _g[i])edges[i].Add(new Edge(i,j,_e()));}public Graph(int[][]_g,Func<T>_e){n=_g.Length;edges=new List<Edge>[n];for(int i=0;i<n;i++)edges[i]=new List<Edge>();for(int i=0;i<n;i++)foreach(var j in _g[i])edges[i].Add(new Edge(i,j,_e()));}public Graph(int _n){n=_n;edges=new List<Edge>[n];for(int i=0;i<n;i++)edges[i]=new List<Edge>();}public void AddEdge(int x,int y,T data){edges[x].Add(new Edge(x,y,data));edges[y].Add(new Edge(y,x,data));}public void AddDirectedEdge(int src,int to,T data){edges[src].Add(new Edge(src,to,data));}public Edge[][]ToArray(bool sort=true){if(sort)for(int i=0;i<n;i++)edges[i].Sort((e,f)=>e.to.CompareTo(f.to));var g=new Edge[n][];for(int i=0;i<n;i++)g[i]=edges[i].ToArray();return g;}public int[][]ToUnweightedArray(bool sort=true){if(sort)for(int i=0;i<n;i++)edges[i].Sort((e,f)=>e.to.CompareTo(f.to));var g=new int[n][];for(int i=0;i<n;i++)g[i]=edges[i].Select(e=>e.to).ToArray();return g;}public(Edge[]csr,int[]start)ToCSR(bool sort=true){if(sort)for(int i=0;i<n;i++)edges[i].Sort((e,f)=>e.to.CompareTo(f.to));var start=new int[n+1];for(int i=0;i<n;i++)start[i+1]=start[i]+edges[i].Count;var csr=new Edge[start[n]];for(int i=0;i<n;i++)for(int j=0;j<edges[i].Count;j++)csr[j+start[i]]=edges[i][j];return(csr,start);}public(int[]csr,int[]csr_start)ToUnweightedCSR(bool sort=true){if(sort)for(int i=0;i<n;i++)edges[i].Sort((e,f)=>e.to.CompareTo(f.to));var start=new int[n+1];for(int i=0;i<n;i++)start[i+1]=start[i]+edges[i].Count;var csr=new int[start[n]];for(int i=0;i<n;i++)for(int j=0;j<edges[i].Count;j++)csr[j+start[i]]=edges[i][j].to;return(csr,start);}}}
namespace Lib.GraphLib{public class CentroidDecomposition{private int n;private UnweightedGraph graph;private bool[]used;private int[]csr,csr_start;private int[]sz,par,ord,ord_rev,in_time;private int time;public CentroidDecomposition(int node_size){n=node_size;graph=new UnweightedGraph(n);}public CentroidDecomposition(in UnweightedGraph g){n=g.Size;graph=g;Build();}public void AddEdge(int x,int y)=>graph.AddEdge(x,y);public int GetParent(int x)=>par[x];public ReadOnlySpan<int>GetParentSpan()=>par;public int GetOrder(int x)=>ord[x];public ReadOnlySpan<int>GetOrderSpan()=>ord;public int GetReversedOrder(int x)=>ord_rev[x];public ReadOnlySpan<int>GetReversedOrderSpan()=>ord_rev;public int GetInTime(int x)=>in_time[x];public ReadOnlySpan<int>GetInTimeSpan()=>in_time;SimpleIntPairStack st;public void Build(){used=new bool[n];sz=new int[n];par=new int[n];Array.Fill(par,-1);ord=new int[n];in_time=new int[n];st=new SimpleIntPairStack(n);(csr,csr_start)=graph.ToCSR();DFS(0,-1);ord_rev=ord.Reverse().ToArray();}private void CalcSize(int x,int p){sz[x]=1;var es=csr.AsSpan(csr_start[x],csr_start[x+1]-csr_start[x]);foreach(var y in es){if(!used[y]&&y!=p){CalcSize(y,x);sz[x]+=sz[y];}}}private void DFS(int x,int p0){st.Push((x,-1));while(st.Count>0){var(x1,p1)=st.Pop();if(x1<0){if(p1!=-1)sz[p1]+=sz[~x1];}else{st.Push((~x1,p1));sz[x1]=1;var es=csr.AsSpan(csr_start[x1],csr_start[x1+1]-csr_start[x1]);foreach(var y in es)if(!used[y]&&y!=p1)st.Push((y,x1));}}int tot=sz[x];bool ok=false;int p=-1;while(!ok){ok=true;var es=csr.AsSpan(csr_start[x],csr_start[x+1]-csr_start[x]);foreach(var y in es){if(!used[y]&&y!=p&&2*sz[y]>tot){p=x;x=y;ok=false;break;}}}par[x]=p0;ord[time]=x;in_time[x]=time++;used[x]=true;{var es=csr.AsSpan(csr_start[x],csr_start[x+1]-csr_start[x]);foreach(var y in es)if(!used[y])DFS(y,x);}}}}
namespace Lib.GraphLib{public class LowestCommonAncestor{public int Size{get;private set;}public readonly int Root;readonly UnweightedGraph graph;int[][]g;SparseTable<(int x,int d)>sparse_table;internal int[]in_time,depth,parent,euler_tour;private int time;public LowestCommonAncestor(int size,int root=0){Size=size;Root=root;graph=new UnweightedGraph(size);}public LowestCommonAncestor(in UnweightedGraph graph,int root=0){Size=graph.Size;Root=root;this.graph=graph;Build();}public void AddEdge(int u,int v)=>graph.AddEdge(u,v);public void Build(){g=graph.ToArray();parent=new int[Size];Array.Fill(parent,-1);depth=new int[Size];in_time=new int[Size];euler_tour=new int[2*Size-1];time=0;DFS(Root);var pair=new(int x,int d)[euler_tour.Length];for(int i=0;i<euler_tour.Length;i++)pair[i]=(euler_tour[i],depth[euler_tour[i]]);sparse_table=new SparseTable<(int x,int d)>(pair,(x,y)=>x.d<=y.d?x:y);}private void DFS(int x){in_time[x]=time;euler_tour[time++]=x;foreach(var y in g[x]){if(y==parent[x])continue;parent[y]=x;depth[y]=depth[x]+1;DFS(y);euler_tour[time++]=x;}}public int LCA(int u,int v){int x=in_time[u],y=in_time[v];if(x>y)(x,y)=(y,x);return sparse_table[x..(y+1)].x;}}}
namespace Lib{public class UnweightedGraph:Graph<int>{public UnweightedGraph(UnweightedGraph _g):base(_g){}public UnweightedGraph(List<int>[]_g):base(_g,()=>1){}public UnweightedGraph(int _n):base(_n){}[MethodImpl(256)]public void AddEdge(int x,int y)=>AddEdge(x,y,1);[MethodImpl(256)]public void AddDirectedEdge(int src,int to)=>AddDirectedEdge(src,to,1);public new int[][]ToArray(bool sort=true)=>ToUnweightedArray(sort);public new(int[]csr,int[]csr_start)ToCSR(bool sort=true)=>ToUnweightedCSR(sort);}}
namespace Lib{public interface IGroup<T>:IMonoid<T>,IInvertible<T>{}public struct IntAddGroup:IMonoid<int>,IGroup<int>{public int Identity=>0;public int Operate(int x,int y)=>x+y;public int Inverse(int x)=>-x;}public struct LongAddGroup:IMonoid<long>,IGroup<long>{public long Identity=>0;public long Operate(long x,long y)=>x+y;public long Inverse(long x)=>-x;}public struct ModIntAddGroup<T>:IMonoid<StaticModInt<T>>,IGroup<StaticModInt<T>>where T:struct,IStaticMod{public StaticModInt<T>Identity=>0;public StaticModInt<T>Operate(StaticModInt<T>x,StaticModInt<T>y)=>x+y;public StaticModInt<T>Inverse(StaticModInt<T>x)=>-x;}public struct IntPairAddGroup:IMonoid<(int,int)>,IGroup<(int,int)>{public(int,int)Identity=>(0,0);public(int,int)Operate((int,int)x,(int,int)y)=>(x.Item1+y.Item1,x.Item2+y.Item2);public(int,int)Inverse((int,int)x)=>(-x.Item1,-x.Item2);}public struct LongPairAddGroup:IMonoid<(long,long)>,IGroup<(long,long)>{public(long,long)Identity=>(0,0);public(long,long)Operate((long,long)x,(long,long)y)=>(x.Item1+y.Item1,x.Item2+y.Item2);public(long,long)Inverse((long,long)x)=>(-x.Item1,-x.Item2);}}
namespace Lib{public interface IMonoid<T>:IOperation<T>,IIdentity<T>{}public struct IntMinMonoid:IMonoid<int>{public int Identity=>int.MaxValue;public int Operate(int x,int y)=>Math.Min(x,y);}public struct IntMaxMonoid:IMonoid<int>{public int Identity=>int.MinValue;public int Operate(int x,int y)=>Math.Max(x,y);}public struct LongMinMonoid:IMonoid<long>{public long Identity=>long.MaxValue;public long Operate(long x,long y)=>Math.Min(x,y);}public struct LongMaxMonoid:IMonoid<long>{public long Identity=>long.MinValue;public long Operate(long x,long y)=>Math.Max(x,y);}public struct PairMonoid<T1,Op1,T2,Op2>:IMonoid<(T1,T2)>where Op1:struct,IMonoid<T1>where Op2:struct,IMonoid<T2>{public readonly static Op1 op1=default;public readonly static Op2 op2=default;public(T1,T2)Identity=>(op1.Identity,op2.Identity);public(T1,T2)Operate((T1,T2)x,(T1,T2)y)=>(op1.Operate(x.Item1,y.Item1),op2.Operate(x.Item2,y.Item2));}public struct Tuple2Monoid<T,Op>:IMonoid<(T,T)>where Op:struct,IMonoid<T>{public readonly static Op op=default;public(T,T)Identity=>(op.Identity,op.Identity);public(T,T)Operate((T,T)x,(T,T)y)=>(op.Operate(x.Item1,y.Item1),op.Operate(x.Item2,y.Item2));}public struct Tuple3Monoid<T,Op>:IMonoid<(T,T,T)>where Op:struct,IMonoid<T>{public readonly static Op op=default;public(T,T,T)Identity=>(op.Identity,op.Identity,op.Identity);public(T,T,T)Operate((T,T,T)x,(T,T,T)y)=>(op.Operate(x.Item1,y.Item1),op.Operate(x.Item2,y.Item2),op.Operate(x.Item3,y.Item3));}public struct Tuple4Monoid<T,Op>:IMonoid<(T,T,T,T)>where Op:struct,IMonoid<T>{public readonly static Op op=default;public(T,T,T,T)Identity=>(op.Identity,op.Identity,op.Identity,op.Identity);public(T,T,T,T)Operate((T,T,T,T)x,(T,T,T,T)y)=>(op.Operate(x.Item1,y.Item1),op.Operate(x.Item2,y.Item2),op.Operate(x.Item3,y.Item3),op.Operate(x.Item4,y.Item4));}}
namespace Lib{public interface IIdentity<T>{T Identity{get;}}}
namespace Lib{public interface IInvertible<T>{T Inverse(T x);}}
namespace Lib{public interface IOperation<T>{T Operate(T x,T y);}}
namespace Lib{public partial class StreamScanner{public StreamScanner(Stream stream){str=stream;}private readonly Stream str;private readonly byte[]buf=new byte[1024];private int len,ptr;public bool isEof=false;public bool IsEndOfStream{get{return isEof;}}[MethodImpl(256)]private byte Read(){if(isEof)throw new EndOfStreamException();if(ptr>=len){ptr=0;if((len=str.Read(buf,0,1024))<=0){isEof=true;return 0;}}return buf[ptr++];}[MethodImpl(256)]public char Char(){byte b;do b=Read();while(b<33||126<b);return(char)b;}[MethodImpl(256)]public string Line(){var sb=new StringBuilder();for(var b=Char();b!=10&&!isEof;b=(char)Read())sb.Append(b);return sb.ToString();}[MethodImpl(256)]public string Scan(){var sb=new StringBuilder();for(var b=Char();b>=33&&b<=126;b=(char)Read())sb.Append(b);return sb.ToString();}[MethodImpl(256)]public long Integer(){long ret=0;var ng=false;byte b;do b=Read();while(b!='-'&&(b<'0'||'9'<b));if(b=='-'){ng=true;b=Read();}for(;'0'<=b&&b<='9';b=Read())ret=ret*10+(b^'0');return ng?-ret:ret;}[MethodImpl(256)]public ulong UInteger(){ulong ret=0;byte b;do b=Read();while(b<'0'||'9'<b);for(;'0'<=b&&b<='9';b=Read())ret=ret*10+(ulong)(b^'0');return ret;}[MethodImpl(256)]public double Double()=>double.Parse(Scan());}}
namespace Lib{public interface IStaticMod{uint Mod{get;}bool IsPrime{get;}}public readonly struct Mod1000000007:IStaticMod{public uint Mod=>1000000007;public bool IsPrime=>true;}public readonly struct Mod998244353:IStaticMod{public uint Mod=>998244353;public bool IsPrime=>true;}}
namespace Lib{public readonly struct StaticModInt<T>:IEquatable<StaticModInt<T>>where T:struct,IStaticMod{internal readonly uint _v;private static readonly T op=default;public int Value=>(int)_v;public static int Mod=>(int)op.Mod;public static StaticModInt<T>Zero=>default;public static StaticModInt<T>One=>new StaticModInt<T>(1u);[MethodImpl(256)]public static StaticModInt<T>Raw(int v){var u=unchecked((uint)v);return new StaticModInt<T>(u);}[MethodImpl(256)]public StaticModInt(long v):this(Round(v)){}[MethodImpl(256)]public StaticModInt(ulong v):this((uint)(v%op.Mod)){}[MethodImpl(256)]private StaticModInt(uint v)=>_v=v;public static bool IsZero(StaticModInt<T>x)=>x.Value==0;public static bool IsOne(StaticModInt<T>x)=>x.Value==1;[MethodImpl(256)]private static uint Round(long v){var x=v%op.Mod;if(x<0)x+=op.Mod;return(uint)x;}[MethodImpl(256)]public static StaticModInt<T>operator ++(StaticModInt<T>v){var x=v._v+1;if(x==op.Mod)x=0;return new StaticModInt<T>(x);}[MethodImpl(256)]public static StaticModInt<T>operator --(StaticModInt<T>v){var x=v._v;if(x==0)x=op.Mod;return new StaticModInt<T>(x-1);}[MethodImpl(256)]public static StaticModInt<T>operator+(StaticModInt<T>lhs,StaticModInt<T>rhs){var v=lhs._v+rhs._v;if(v>=op.Mod)v-=op.Mod;return new StaticModInt<T>(v);}[MethodImpl(256)]public static StaticModInt<T>operator-(StaticModInt<T>lhs,StaticModInt<T>rhs){unchecked{var v=lhs._v-rhs._v;if(v>=op.Mod)v+=op.Mod;return new StaticModInt<T>(v);}}[MethodImpl(256)]public static StaticModInt<T>operator*(StaticModInt<T>lhs,StaticModInt<T>rhs)=>new StaticModInt<T>((uint)((ulong)lhs._v*rhs._v%op.Mod));[MethodImpl(256)]public static StaticModInt<T>operator/(StaticModInt<T>lhs,StaticModInt<T>rhs)=>new StaticModInt<T>((uint)((ulong)lhs._v*Inv(rhs._v)%op.Mod));[MethodImpl(256)]public static StaticModInt<T>operator+(StaticModInt<T>v)=>v;[MethodImpl(256)]public static StaticModInt<T>operator-(StaticModInt<T>v)=>new StaticModInt<T>(v._v==0?0:op.Mod-v._v);[MethodImpl(256)]public static bool operator==(StaticModInt<T>lhs,StaticModInt<T>rhs)=>lhs._v==rhs._v;[MethodImpl(256)]public static bool operator!=(StaticModInt<T>lhs,StaticModInt<T>rhs)=>lhs._v!=rhs._v;[MethodImpl(256)]public static implicit operator StaticModInt<T>(int v)=>new StaticModInt<T>(v);[MethodImpl(256)]public static implicit operator StaticModInt<T>(uint v)=>new StaticModInt<T>((long)v);[MethodImpl(256)]public static implicit operator StaticModInt<T>(long v)=>new StaticModInt<T>(v);[MethodImpl(256)]public static implicit operator StaticModInt<T>(ulong v)=>new StaticModInt<T>(v);[MethodImpl(256)]public static implicit operator long(StaticModInt<T>v)=>v._v;[MethodImpl(256)]public static implicit operator ulong(StaticModInt<T>v)=>v._v;[MethodImpl(256)]public StaticModInt<T>Pow(long n){var x=this;var r=new StaticModInt<T>(1U);if(n<0)(x,n)=(x.Inv(),-n);while(n>0){if((n&1)>0)r*=x;x*=x;n>>=1;}return r;}[MethodImpl(256)]public StaticModInt<T>Inv()=>new StaticModInt<T>(Inv(_v));[MethodImpl(256)]static ulong Inv(ulong x){long u=op.Mod,xu=1,yu=0,v=(long)x,xv=0,yv=1;while(v!=0){long w=SafeMod(u,v);long q=(u-w)/v;long xw=xu-xv*q;long yw=yu-yv*q;u=v;xu=xv;yu=yv;v=w;xv=xw;yv=yw;}return(ulong)(yu<0?yu+op.Mod:yu);}[MethodImpl(256)]static long SafeMod(long x,long m){long r=x%m;if(r<0)r+=m;return r;}[MethodImpl(256)]public override string ToString()=>_v.ToString();[MethodImpl(256)]public string ToString(string format,IFormatProvider formatProvider)=>_v.ToString(format,formatProvider);[MethodImpl(256)]public override bool Equals(object?obj)=>obj is StaticModInt<T>m&&Equals(m);[MethodImpl(256)]public bool Equals(StaticModInt<T>other)=>_v==other._v;[MethodImpl(256)]public override int GetHashCode()=>_v.GetHashCode();}}
namespace Lib{public static class OutputLib{[MethodImpl(256)]public static void WriteJoin<T>(string s,IEnumerable<T>t)=>Console.WriteLine(string.Join(s,t));[MethodImpl(256)]public static void WriteMat<T>(T[,]a,string sep=" "){int sz1=a.GetLength(0),sz2=a.GetLength(1);var b=new T[sz2];for(int i=0;i<sz1;i++){for(int j=0;j<sz2;j++)b[j]=a[i,j];WriteJoin(sep,b);}}[MethodImpl(256)]public static void WriteMat<T>(T[][]a,string sep=" "){foreach(var ar in a)WriteJoin(sep,ar);}[MethodImpl(256)]public static void WriteMat<T>(T[][]a,Func<T,string>map,string sep=" "){foreach(var ar in a)WriteJoin(sep,ar.Select(x=>map(x)));}[MethodImpl(256)]public static void Write(object t)=>Console.WriteLine(t.ToString());[MethodImpl(256)]public static void Write(params object[]arg)=>Console.WriteLine(string.Join(" ",arg.Select(x=>x.ToString())));[MethodImpl(256)]public static void Write(string str)=>Console.WriteLine(str);[MethodImpl(256)]public static void WriteFlush(object t){Console.WriteLine(t.ToString());Console.Out.Flush();}[MethodImpl(256)]public static void WriteError(object t)=>Console.Error.WriteLine(t.ToString());[MethodImpl(256)]public static void Flush()=>Console.Out.Flush();[MethodImpl(256)]public static void YN(bool t)=>Console.WriteLine(t?"YES":"NO");[MethodImpl(256)]public static void Yn(bool t)=>Console.WriteLine(t?"Yes":"No");[MethodImpl(256)]public static void yn(bool t)=>Console.WriteLine(t?"yes":"no");[MethodImpl(256)]public static void DeleteLine()=>Console.Write("\x1b[1A\x1b[2K");[MethodImpl(256)]public static void ProgressBar(long now,long total,int blocks=50){int x=(int)((2*now*blocks+1)/(2*total));Console.Write($"\x1b[G[\x1b[42m{string.Concat(Enumerable.Repeat("_",x))}\x1b[0m{string.Concat(Enumerable.Repeat("_",blocks-x))}] : {now} / {total}");}}}
namespace SourceExpander{public class Expander{[Conditional("EXP")]public static void Expand(string inputFilePath=null,string outputFilePath=null,bool ignoreAnyError=true){}public static string ExpandString(string inputFilePath=null,bool ignoreAnyError=true){return "";}}}
#endregion Expanded by https://github.com/kzrnm/SourceExpander