結果
| 問題 | No.1419 Power Moves |
| ユーザー |
 eSeF
|
| 提出日時 | 2021-03-17 21:11:44 |
| 言語 | C#(csc) (csc 3.9.0) |
| 結果 |
AC
|
| 実行時間 | 319 ms / 2,000 ms |
| コード長 | 56,499 bytes |
| コンパイル時間 | 4,993 ms |
| コンパイル使用メモリ | 123,008 KB |
| 実行使用メモリ | 23,772 KB |
| 最終ジャッジ日時 | 2024-11-15 16:00:49 |
| 合計ジャッジ時間 | 11,989 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 31 ms
19,584 KB |
| testcase_01 | AC | 30 ms
19,200 KB |
| testcase_02 | AC | 31 ms
19,456 KB |
| testcase_03 | AC | 30 ms
19,456 KB |
| testcase_04 | AC | 31 ms
19,200 KB |
| testcase_05 | AC | 29 ms
19,200 KB |
| testcase_06 | AC | 30 ms
19,328 KB |
| testcase_07 | AC | 29 ms
19,456 KB |
| testcase_08 | AC | 28 ms
19,072 KB |
| testcase_09 | AC | 225 ms
23,384 KB |
| testcase_10 | AC | 36 ms
19,712 KB |
| testcase_11 | AC | 62 ms
21,888 KB |
| testcase_12 | AC | 268 ms
23,372 KB |
| testcase_13 | AC | 243 ms
23,244 KB |
| testcase_14 | AC | 238 ms
23,452 KB |
| testcase_15 | AC | 244 ms
23,324 KB |
| testcase_16 | AC | 244 ms
23,456 KB |
| testcase_17 | AC | 33 ms
19,328 KB |
| testcase_18 | AC | 31 ms
19,200 KB |
| testcase_19 | AC | 29 ms
19,328 KB |
| testcase_20 | AC | 288 ms
23,488 KB |
| testcase_21 | AC | 310 ms
23,500 KB |
| testcase_22 | AC | 284 ms
23,496 KB |
| testcase_23 | AC | 276 ms
23,496 KB |
| testcase_24 | AC | 282 ms
23,772 KB |
| testcase_25 | AC | 271 ms
23,372 KB |
| testcase_26 | AC | 319 ms
23,376 KB |
| testcase_27 | AC | 273 ms
23,496 KB |
| testcase_28 | AC | 272 ms
23,368 KB |
| testcase_29 | AC | 275 ms
23,620 KB |
| testcase_30 | AC | 317 ms
23,496 KB |
| testcase_31 | AC | 302 ms
23,616 KB |
| testcase_32 | AC | 265 ms
23,624 KB |
| testcase_33 | AC | 264 ms
23,244 KB |
コンパイルメッセージ
Microsoft (R) Visual C# Compiler version 3.9.0-6.21124.20 (db94f4cc) Copyright (C) Microsoft Corporation. All rights reserved.
ソースコード
using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using System.Numerics;
using System.Threading;
using System.Runtime.CompilerServices;
using System.Diagnostics;
using static System.Math;
using static System.Array;
using static AtCoder.Cout;
using static AtCoder.Tool;
using static AtCoder.Graph;
using ModInt = AtCoder_MOD.ModInt<AtCoder_MOD.Mod1000000007>;using static AtCoder_MOD.ModCalc<AtCoder_MOD.Mod1000000007>;using MOD_Matrix = AtCoder_MOD.MOD_Matrix<AtCoder_MOD.Mod1000000007>;
//using ModInt = AtCoder_MOD.ModInt<AtCoder_MOD.Mod998244353>;using static AtCoder_MOD.ModCalc<AtCoder_MOD.Mod998244353>;using MOD_Matrix = AtCoder_MOD.MOD_Matrix<AtCoder_MOD.Mod998244353>;
namespace AtCoder
{
class AC
{
static readonly int MOD = ModInt.GetMod();
const int INF = int.MaxValue / 2;
const long SINF = long.MaxValue / 3;
static readonly int[] dI = { 0, 1, 0, -1, 1, -1, -1, 1 };
static readonly int[] dJ = { 1, 0, -1, 0, 1, 1, -1, -1 };
static bool isInside(int i, int H, int j, int W) => 0 <= i && i < H && 0 <= j && j < W;
static void Main(string[] args)
{
//var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }; Console.SetOut(sw);
var th = new Thread(Run, 1 << 26);
/*th.Start();
th.Join();*/
Run();
Console.Out.Flush();
}
static void Run()
{
int Testcase = 1;
//Testcase = Cin.Int;
for (var testcase_id = 0; testcase_id < Testcase; testcase_id++)
{
Solve(testcase_id);
}
}
static void Solve(int testcase_id)
{
Cin.Scanf(out int N, out int K);
var st = (N - F_mp(2, K, N) + 1) % N;
//OutL(F_mp(2, K, N));
var w = new int[N];Fill(w, -1);
//OutL($"st={st}");
for(var i = 0; w[(st + i) % N] == -1; i += 2)
{
w[(st + i) % N] = i / 2;
}
//Out_Sep(w);
BigInteger T = w.Count(x => x != -1);
//(2^K - 1)/T mod MOD
BigInteger M = MOD * T;
BigInteger S = 1, P = 2;
int e = K;
while (e > 0)
{
if ((e & 1) != 0) S = (S * P) % M;
P = (P * P) % M;
e >>= 1;
}
ModInt all = ModPow(2, K);
for(var i = 0; i < N; i++)
{
if (w[i] == -1) { OutL(0); }
else
{
ModInt ans = (long)((S - w[i] + T - 1) / T);
OutL(ans / all);
}
}
}
}
public struct Edge
{
public int from, to;
public long w;
public double dw;
public Edge(int to, long weight) { this.to = to; w = weight; from = -1; dw = -1; }
public Edge(int from, int to, long weight) { this.from = from; this.to = to; w = weight; dw = -1; }
public Edge(int to, double weight) { this.to = to; from = -1; w = -1; dw = weight; }
}
public struct Matrix<T>
{
public int H, W;
public T[] mat;
public static T Ip { set; get; }
public static T Im { set; get; }
public static Func<T, T, T> fp { set; get; }
public static Func<T, T, T> fm { set; get; }
public Matrix(int sizeH, int sizeW)
{
H = sizeH;
W = sizeW;
mat = new T[H * W];
//Fill(mat, default);
}
public Matrix(int sizeH,int sizeW, T[][] init)
{
H = sizeH;
W = sizeW;
mat = new T[H * W];
for (var i = 0; i < H; i++) for (var j = 0; j < W; j++) mat[i * W + j] = init[i][j];
}
public Matrix(int sizeH, int sizeW, T[,] init)
{
H = sizeH;
W = sizeW;
mat = new T[H * W];
for (var i = 0; i < H; i++) for (var j = 0; j < W; j++) mat[i * W + j] = init[i, j];
}
public static void SetUnit(Func<T, T, T> FP, T IP, Func<T, T, T> FM, T IM)
{
fp = FP;Ip = IP;
fm = FM;Im = IM;
}
public T this[int idh,int idw]
{
set
{
Debug.Assert(0 <= idh && idh < H && 0 <= idw && idw < W);
mat[idh * W + idw] = value;
}
get
{
Debug.Assert(0 <= idh && idh < H && 0 <= idw && idw < W);
return mat[idh * W + idw];
}
}
public static Matrix<T> operator +(Matrix<T> m1, Matrix<T> m2)
{
Debug.Assert(m1.H == m2.H && m1.W == m2.W);
for (var i = 0; i < m1.H; i++) for (var j = 0; j < m1.W; j++)
m1[i, j] = fp(m1[i, j], m2[i, j]);
return m1;
}
public static Matrix<T> operator *(Matrix<T> m1, Matrix<T> m2)
{
Debug.Assert(m1.W == m2.H);
var ret = new Matrix<T>(m1.H, m2.W);
for(var i = 0; i < m1.H; i++)
{
for(var j = 0; j < m2.W; j++)
{
ret[i, j] = default;
for (var k = 0; k < m1.W; k++) ret[i, j] = fp(ret[i, j], fm(m1[i, k], m2[k, j]));
}
}
return ret;
}
public Matrix<T> Pow(long K)
{
Debug.Assert(H == W);
int n = H;
Debug.Assert(K >= 0);
var ret = new Matrix<T>(n, n);
for (var i = 0; i < n; i++) ret[i, i] = Im;
if (K == 0) return ret;
var P = new Matrix<T>(n, n);
for (var i = 0; i < n; i++) for (var j = 0; j < n; j++) P[i, j] = this[i, j];
while (K > 0)
{
if ((K & 1) != 0) ret *= P;
P *= P;
K >>= 1;
}
return ret;
}
public override string ToString()
{
var str = new StringBuilder();
for(var i = 0; i < H; i++)
{
for(var j = 0; j < W; j++)
{
if (j == W - 1) str.Append($"{this[i, j]}\n");
else str.Append($"{this[i, j]} ");
}
}
return str.ToString();
}
}
public static class Graph
{
const long inf = long.MaxValue / 3;
public static List<List<T>> Gen_Graph<T>(int size)
{
var ret = new List<List<T>>();
for (var i = 0; i < size; i++) ret.Add(new List<T>());
return ret;
}
public static long[] Dijkstra(List<List<Edge>> G, int st)
{
int N = G.Count();
long[] ret = new long[N];
var V = new Priority_Queue<Tuple<long, int>>((x, y) => Sig(x.Item1 - y.Item1));
for (var i = 0; i < N; i++) ret[i] = inf;
ret[st] = 0; V.Enqueue(new Tuple<long, int>(0, st));
while (V.Any())
{
var cur = V.Dequeue();
int v = cur.Item2;
long cd = cur.Item1;
if (ret[v] < cd) continue;
foreach (var ed in G[v])
{
if (ret[ed.to] > cd + ed.w)
{
ret[ed.to] = cd + ed.w;
V.Enqueue(new Tuple<long, int>(ret[ed.to], ed.to));
}
}
}
return ret;
}
public static long[] Bellman_Frod(List<Edge> E, int st, int N, out bool neg_close)
{
var ret = new long[N];
for (var i = 0; i < N; i++) ret[i] = inf;
ret[st] = 0;
for (var i = 0; i < N; i++)
{
foreach (var ed in E)
{
if (ret[ed.from] != inf && ret[ed.to] > ret[ed.from] + ed.w)
{
if (i == N - 1) { neg_close = true; return ret; }
ret[ed.to] = ret[ed.from] + ed.w;
}
}
}
neg_close = false;
return ret;
}
}
public class SCC
{
int n;
struct Edge_S { public int from, to; public Edge_S(int f, int t) { from = f; to = t; } }
List<Edge_S> E;
int[] id;
public SCC(int size) { n = size; E = new List<Edge_S>(); }
public void Add_Edge(int from, int to)
{
E.Add(new Edge_S(from, to));
}
public int[][] Scc_Result()
{
var start = new int[n + 1];
var nxt = new int[E.Count];
//var scc = new List<List<int>>();
foreach (var ed in E) start[ed.from + 1]++;
for (var i = 0; i < n; i++) start[i + 1] += start[i];
var itr = new int[n + 1]; for (var i = 0; i <= n; i++) itr[i] = start[i];
foreach (var ed in E) nxt[itr[ed.from]++] = ed.to;
int now = 0;
int[] ord = new int[n];
int[] low = new int[n];
id = new int[n];
var V = new Stack<int>();
for (var i = 0; i < n; i++) ord[i] = -1;
int nowid = 0;
Action<int> DFS = null;
DFS = (v) =>
{
low[v] = ord[v] = now++;
V.Push(v);
for (var i = start[v]; i < start[v + 1]; i++)
{
var nx = nxt[i];
if (ord[nx] == -1)
{
DFS(nx);
low[v] = Min(low[v], low[nx]);
}
else
{
low[v] = Min(low[v], ord[nx]);
}
}
if (low[v] == ord[v])
{
while (true)
{
var u = V.Pop();
id[u] = nowid;
ord[u] = n + 1;
if (u == v) break;
}
nowid++;
}
};
for (var i = 0; i < n; i++) if (ord[i] == -1) DFS(i);
for (var i = 0; i < n; i++)
{
id[i] = nowid - 1 - id[i];
itr[i] = 0;
}
var scc = new int[nowid][];
for (var i = 0; i < n; i++) itr[id[i]]++;
for (var i = 0; i < nowid; i++) scc[i] = new int[itr[i]];
for (var i = 0; i < n; i++) scc[id[i]][--itr[id[i]]] = i;
/*
for (var i = 0; i < nowid; i++) scc.Add(new List<int>());
for (var i = 0; i < n; i++) scc[id[i]].Add(i);*/
return scc;
}
public int v_id(int v) => id[v];
}
public class Two_SAT
{
// use with SCC Library
int n;
bool[] result;
SCC scc;
readonly int md;
public Two_SAT(int size)
{
n = size;
result = new bool[n];
scc = new SCC(n << 1);
md = n << 1;
}
public void Add_Closure(int i, bool fi, int j, bool fj)
{
if (!fi) i += n;
if (!fj) j += n;
scc.Add_Edge((i + n) % md, j);
scc.Add_Edge((j + n) % md, i);
}
public bool Satisfy()
{
scc.Scc_Result();
for (var i = 0; i < n; i++)
{
int j = scc.v_id(i), k = scc.v_id(i + n);
if (j == k) return false;
result[i] = j > k;
}
return true;
}
public bool[] ans() => result;
}
public class Dinic
{
readonly int n;
const int inf = int.MaxValue / 2;
public class Edge_F
{
public int _to { get; set; }
public long _cap { get; set; }
public int _rev { get; set; }
public Edge_F(int to, long cap, int rev) { _to = to; _cap = cap; _rev = rev; }
}
List<List<Edge_F>> G;
int[] level, itr;
public Dinic(int vertice)
{
n = vertice;
level = new int[n];
itr = new int[n];
G = new List<List<Edge_F>>();
for (var _ = 0; _ < n; _++) G.Add(new List<Edge_F>());
}
/*================ ^ _ ^ ==================*/
//辺の追加（from->to,容量cap）
public void Add_Edge(int from, int to, long cap)
{
G[from].Add(new Edge_F(to, cap, G[to].Count()));
G[to].Add(new Edge_F(from, 0, G[from].Count() - 1));
}
//bfsパート（levelの設定）
void Bfs(int s)
{
//Fillはバージョン古いと使えないため...
for (var i = 0; i < n; i++) level[i] = -1;
level[s] = 0;
var Q = new Queue<int>();
Q.Enqueue(s);
while (Q.Any())
{
int v = Q.Dequeue();
foreach (var ed in G[v])
{
if (ed._cap > 0 && level[ed._to] == -1)
{
level[ed._to] = level[v] + 1;
Q.Enqueue(ed._to);
}
}
}
}
//dfsパート（増加パスの探索）
long Dfs(int v, int t, long f)
{
if (v == t) return f;
for (var i = itr[v]; i < G[v].Count(); i++)
{
itr[v] = i;
var ed = G[v][i];
if (ed._cap > 0 && level[v] < level[ed._to])
{
var d = Dfs(ed._to, t, Min(f, ed._cap));
if (d > 0)
{
ed._cap -= d;
G[ed._to][ed._rev]._cap += d;
return d;
}
}
}
return 0;
}
//s->tの最大流を返す
//一般:O(N^2M)
//二部グラフマッチング:O(M*Sqrt(N))
//辺の容量が全て同じ:O(min(n^{2/3},m^{1/2})*m)
//になるらしい
public long Max_Flow(int s, int t)
{
long ret = 0;
for (; ; )
{
Bfs(s);
if (level[t] == -1) return ret;
for (var i = 0; i < n; i++) itr[i] = 0;
var flow = 0L;
do { ret += flow; flow = Dfs(s, t, inf); }
while (flow > 0);
}
}
//グラフの状況を返す
public List<List<Edge_F>> GetGraph() => G;
}
public class MinCostFlow
{
const long inf = long.MaxValue / 3;
int n;
public class Edge
{
public int _to, _cap, _rev;
public long _cost;
public bool _isrev;
public Edge(int to, int cap, long cost, int rev, bool isrev)
{
_to = to; _cap = cap; _rev = rev; _cost = cost; _isrev = isrev;
}
}
List<List<Edge>> G;
public MinCostFlow(int size)
{
n = size;
G = new List<List<Edge>>();
for (var i = 0; i < n; i++) G.Add(new List<Edge>());
}
/*辺の追加*/
public void Add_Edge(int s, int t, int cap, long cost)
{
G[s].Add(new Edge(t, cap, cost, G[t].Count(), false));
G[t].Add(new Edge(s, 0, -cost, G[s].Count() - 1, true));
}
public long MinCost(int s, int t, int f)
{
long ret = 0;
var h = new long[n];
var dist = new long[n];
var pre_v = new int[n];
var pre_e = new int[n];
var V = new Priority_Queue<(long, int)>((x, y) => Sig(x.Item1 - y.Item1));
while (f > 0)
{
for (var i = 0; i < n; i++) { dist[i] = inf; pre_v[i] = pre_e[i] = -1; }
dist[s] = 0;
V.Enqueue((0, s));
while (V.Any())
{
var (cd, v) = V.Dequeue();
if (dist[v] < cd) continue;
for (var i = 0; i < G[v].Count(); i++)
{
var ed = G[v][i];
if (ed._cap <= 0) continue;
if (dist[ed._to] + h[ed._to] > cd + h[v] + ed._cost)
{
dist[ed._to] = cd + ed._cost + h[v] - h[ed._to];
pre_v[ed._to] = v;
pre_e[ed._to] = i;
V.Enqueue((dist[ed._to], ed._to));
}
}
}
if (dist[t] == inf) { return -inf; }
for (var i = 0; i < n; i++) h[i] += dist[i];
var nowflow = f;
for (var now = t; now != s; now = pre_v[now])
{
nowflow = Min(nowflow, G[pre_v[now]][pre_e[now]]._cap);
}
f -= nowflow;
ret += nowflow * h[t];
for (var now = t; now != s; now = pre_v[now])
{
var rv = G[pre_v[now]][pre_e[now]]._rev;
G[pre_v[now]][pre_e[now]]._cap -= nowflow;
G[now][rv]._cap += nowflow;
}
}
return ret;
}
public List<List<Edge>> GetEdges() => G;
}
public class LCA
{
List<List<int>> G1;
List<List<Edge>> G2;
int n;
bool isweighted;
int[] dist;
long[] dist_w;
int[,] par;
public LCA(List<List<int>> G)
{
G1 = G;
G2 = null;
n = G1.Count();
isweighted = false;
dist = new int[n];
dist_w = null;
par = new int[25, n];
}
public LCA(List<List<Edge>> G)
{
G1 = null;
G2 = G;
n = G2.Count();
isweighted = true;
dist = new int[n];
dist_w = new long[n];
par = new int[25, n];
}
public void Lca_Build(int root)
{
for (var i = 0; i < n; i++)
{
dist[i] = -1;
if (isweighted) dist_w[i] = -1;
}
var dfs = new Stack<int>();
dfs.Push(root);
dist[root] = 0;
if (isweighted) dist_w[root] = 0;
par[0, root] = -1;
while (dfs.Any())
{
int v = dfs.Pop();
if (isweighted)
{
foreach (var ed in G2[v])
{
if (dist[ed.to] != -1) continue;
par[0, ed.to] = v;
dist_w[ed.to] = dist[v] + ed.w;
dist[ed.to] = dist[v] + 1;
dfs.Push(ed.to);
}
}
else
{
foreach (var nx in G1[v])
{
if (dist[nx] != -1) continue;
par[0, nx] = v;
dist[nx] = dist[v] + 1;
dfs.Push(nx);
}
}
}
for (var i = 1; i < 25; i++)
{
for (var j = 0; j < n; j++)
{
if (par[i - 1, j] == -1) par[i, j] = -1;
else par[i, j] = par[i - 1, par[i - 1, j]];
}
}
}
public int Lca(int u, int v)
{
if (dist[u] < dist[v])
{
var kep = u;
u = v;
v = kep;
}
for (var i = 0; i < 30; i++)
{
if ((((dist[u] - dist[v]) >> i) & 1) != 0)
{
u = par[i, u];
}
}
if (u == v) return u;
for (var i = 24; i >= 0; i--)
{
if (par[i, u] != par[i, v])
{
u = par[i, u];
v = par[i, v];
}
}
return par[0, u];
}
public int[] GetDist() => dist;
public long[] GetWeightedDist() => dist_w;
}
public class Priority_Queue<T>
{
private List<T> Q;
private readonly Comparison<T> Func_Compare;
public Priority_Queue(Comparison<T> comp)
{
Func_Compare = comp;
Q = new List<T>();
}
private void PushHeap(T item)
{
int n = Q.Count();
Q.Add(item);
while (n != 0)
{
int pIndex = (n - 1) / 2;
if (Func_Compare(Q[n], Q[pIndex]) < 0)
{
Swap(n, pIndex);
}
else { break; }
n = pIndex;
}
}
private void PopHeap()
{
int n = Q.Count() - 1;
Q[0] = Q[n];
Q.RemoveAt(n);
int cur = 0;
int comp;
while (2 * cur + 1 <= n - 1)
{
int c1 = 2 * cur + 1;
int c2 = 2 * (cur + 1);
if (c1 == n - 1)
{
comp = c1;
}
else
{
comp = Func_Compare(Q[c1], Q[c2]) < 0 ? c1 : c2;
}
if (Func_Compare(Q[cur], Q[comp]) > 0)
{
Swap(cur, comp);
}
else { break; }
cur = comp;
}
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private void Swap(int a, int b)
{
T keep = Q[a];
Q[a] = Q[b];
Q[b] = keep;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void Enqueue(T value) => PushHeap(value);
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public T Dequeue()
{
T ret = Q[0];
PopHeap();
return ret;
}
public T Peek() => Q[0];
public int Count() => Q.Count();
public bool Any() => Q.Any();
}
public class SegmentTree<T>
{
//1-indexed type
int n;
T[] Tree;
Func<T, T, T> f;
T ex;
int len;
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public SegmentTree(int size, Func<T, T, T> fun, T exvalue)
{
ex = exvalue;
f = fun;
len = size;
n = 1;
while (n < size) n <<= 1;
Tree = new T[n << 1];
for (var i = 0; i < Tree.Length; i++) Tree[i] = ex;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void Set_All()
{
for (var i = n - 1; i >= 1; i--) Tree[i] = f(Tree[i << 1], Tree[(i << 1) | 1]);
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void Assign(int idx, T nxt) => Tree[idx + n] = nxt;
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void Update(int idx)
{
int now = idx + n;
while (now > 1)
{
now >>= 1;
Tree[now] = f(Tree[now << 1], Tree[now << 1 | 1]);
}
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void Query_Update(int idx, T nxt)
{
Assign(idx, nxt); Update(idx);
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void Query_Update_func(int idx, T y)
{
Assign(idx, f(Peek(idx), y)); Update(idx);
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public T Query_Fold(int l, int r)
{
int L = n + l;
int R = n + r;
T vL = ex, vR = ex;
while (L < R)
{
if (L % 2 == 1)
{
vL = f(vL, Tree[L]);
L++;
}
if (R % 2 == 1)
{
vR = f(Tree[R - 1], vR);
R--;
}
L >>= 1;
R >>= 1;
}
return f(vL, vR);
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public T Peek(int idx) => Tree[idx + n];
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void Display(int len)
{
for (var i = 0; i < len; i++) Console.Write($"{Tree[i + n]} ");
Console.WriteLine();
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public int MaxRight(int l, Func<T, bool> ok)
{
if (l == len) { return len; }
l += n;
var sum = ex;
do
{
while (l % 2 == 0) l >>= 1;
if (!ok(f(sum, Tree[l])))
{
while (l < n)
{
l <<= 1;
if (ok(f(sum, Tree[l])))
{
sum = f(sum, Tree[l++]);
}
}
return l - n;
}
sum = f(sum, Tree[l++]);
} while ((l & (-l)) != l);
return len;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public int MinLeft(int r, Func<T, bool> ok)
{
if (r == 0) return 0;
r += n;
var sum = ex;
do
{
r--;
while (r > 1 && (r % 2) != 0) r >>= 1;
if (!ok(f(Tree[r], sum)))
{
while (r < n)
{
r = (r << 1 | 1);
if (ok(f(Tree[r], sum)))
{
sum = f(Tree[r--], sum);
}
}
return r + 1 - n;
}
sum = f(Tree[r], sum);
} while ((r & (-r)) != r);
return 0;
}
}
public class LazySegmentTree<X, A>
{
int n, L;
X[] Tree;
A[] lazy;
Func<X, X, X> fxx;
Func<A, A, A> faa;
Func<X, A, X> fxa;
X exx;
A exa;
public LazySegmentTree(int size, Func<X, X, X> funcxx, Func<A, A, A> funcaa, Func<X, A, X> funcxa, X exval, A exlaz)
{
n = size;
L = (n << 1) - 1;
Tree = new X[n << 1];
lazy = new A[n << 1];
fxx = funcxx;
faa = funcaa;
fxa = funcxa;
exx = exval;
exa = exlaz;
for (var i = 0; i <= L; i++) { Tree[i] = exx; lazy[i] = exa; }
}
public X eval(int id) => fxa(Tree[id], lazy[id]);
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void propagate(int id)
{
int h = 0; while ((1 << (h + 1)) <= id) h++;
for (var n = h; n > 0; n--)
{
int i = id >> n;
Tree[i] = eval(i);
lazy[i << 1] = faa(lazy[i << 1], lazy[i]);
lazy[i << 1 | 1] = faa(lazy[i << 1 | 1], lazy[i]);
lazy[i] = exa;
}
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void re_calc(int id)
{
while (id > 1)
{
id >>= 1;
Tree[id] = fxx(eval(id << 1), eval(id << 1 | 1));
}
}
public void Range_Update(int l, int r, A op)
{
int L = n + l, R = n + r;
int ll = L / (L & (-L));
int rr = R / (R & (-R));
propagate(ll); propagate(rr - 1);
while (L < R)
{
if ((L & 1) == 1)
{
lazy[L] = faa(lazy[L], op);
L++;
}
if ((R & 1) == 1)
{
R--;
lazy[R] = faa(lazy[R], op);
}
L >>= 1; R >>= 1;
}
re_calc(ll); re_calc(rr - 1);
}
public X Range_Get(int l, int r)
{
int L = n + l, R = n + r;
X vL = exx, vR = exx;
propagate(L / (L & (-L)));
propagate(R / (R & (-R)) - 1);
while (L < R)
{
if ((L & 1) == 1)
{
vL = fxx(vL, eval(L));
L++;
}
if ((R & 1) == 1)
{
R--;
vR = fxx(eval(R), vR);
}
L >>= 1; R >>= 1;
}
return fxx(vL, vR);
}
public void Point_Update(int idx, X nxt)
{
int id = idx + n;
propagate(id);
Tree[id] = nxt;
re_calc(id);
}
/*======================*/
public void Assign(int idx, X nxt) => Tree[n + idx] = nxt;
public void Set_All()
{
for (var i = n - 1; i >= 1; i--)
{
Tree[i] = fxx(Tree[i << 1], Tree[i << 1 | 1]);
lazy[i] = faa(lazy[i << 1], lazy[i << 1 | 1]);
}
}
public X Peek(int idx) => Range_Get(idx, idx + 1);
public void Display(int len)
{
for (var i = 0; i < len; i++) Console.Write($"{Range_Get(i, i + 1)} ");
Console.WriteLine();
}
public void Displayall()
{
//木の形で表示、nが2冪でない時は注意
int e = 0;
while ((1 << e) <= n)
{
for (var i = (1 << e); i < (1 << e) + (1 << e); i++) Console.Write($"{Tree[i]}/{lazy[i]} ");
Console.WriteLine();
e++;
}
}
}
public class StringTools
{
public static int[] Z_algorithm(string S)
{
int L = S.Length;
var ret = new int[L];
int i = 1, j = 0;
ret[0] = L;
while (i < L)
{
while (i + j < L && (S[i + j] == S[j])) j++;
ret[i] = j;
if (j == 0) { i++; continue; }
int k = 1;
while (i + k < L && (k + ret[k] < j))
{
ret[i + k] = ret[k];
k++;
}
i += k;
j -= k;
}
return ret;
}
}
public class Rolling_Hash
{
const ulong m30 = (1UL << 30) - 1;
const ulong m31 = (1UL << 31) - 1;
const ulong MOD = (1UL << 61) - 1;
const ulong Pl = (MOD << 1) << 1;
private uint B;
private string S;
ulong[] hash;
ulong[] pw;
public Rolling_Hash(string str)
{
S = str;
B = (uint)new Random().Next(1 << 12 + 1, int.MaxValue);
int L = S.Length;
hash = new ulong[L + 1];
pw = new ulong[L + 1];
hash[0] = 0;
pw[0] = 1;
for (var i = 0; i < L; i++)
{
hash[i + 1] = CalcMod(Mul(hash[i], B) + S[i]);
pw[i + 1] = CalcMod(Mul(pw[i], B));
}
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public ulong GetHashValue(int idx) => hash[idx];
[MethodImpl(MethodImplOptions.AggressiveInlining)]//segment [l,r]
public ulong Hash_fold(int l, int r) => CalcMod(Pl + hash[r + 1] - Mul(hash[l], pw[r - l + 1]));
[MethodImpl(MethodImplOptions.AggressiveInlining)]//segment[start,start+len-1]
public ulong Hash_sub(int start, int len) => CalcMod(Pl + hash[start + len] - Mul(hash[start], pw[len]));
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public ulong[] GetHashArray() => hash;
[MethodImpl(MethodImplOptions.AggressiveInlining)]
ulong Mul(ulong a, ulong b)
{
ulong au = a >> 31;
ulong ad = a & m31;
ulong bu = b >> 31;
ulong bd = b & m31;
ulong mid = ad * bu + au * bd;
ulong midu = mid >> 30;
ulong midd = mid & m30;
return au * bu * 2 + midu + (midd << 31) + ad * bd;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
ulong CalcMod(ulong x)
{
ulong xu = x >> 61;
ulong xd = x & MOD;
ulong res = xu + xd;
if (res >= MOD) res -= MOD;
return res;
}
}
public class UnionFind
{
private int[] parent;
private int[] rank;
private int[] size;
public UnionFind(int n)
{
parent = new int[n];
rank = new int[n];
size = new int[n];
for (var i = 0; i < n; i++)
{
parent[i] = i;
rank[i] = 0;
size[i] = 1;
}
}
public int Root(int x)
{
return parent[x] == x ? x : parent[x] = Root(parent[x]);
}
public bool SameRoot(int x, int y)
{
return Root(x) == Root(y);
}
public void Unite(int x, int y)
{
x = Root(x);
y = Root(y);
if (x == y) { return; }
if (rank[x] < rank[y])
{
parent[x] = y;
size[y] += size[x];
size[x] = 0;
}
else
{
parent[y] = x;
if (rank[x] == rank[y]) { rank[x]++; }
size[x] += size[y];
size[y] = 0;
}
}
public int SizeOf(int x)
{
return size[Root(x)];
}
}
static class Cin
{
public static string[] ReadSplit => Console.ReadLine().Split();
public static int[] ReadSplitInt => ConvertAll(ReadSplit, int.Parse);
public static long[] ReadSplitLong => ConvertAll(ReadSplit, long.Parse);
public static double[] ReadSplit_Double => ConvertAll(ReadSplit, double.Parse);
public static string Str => Console.ReadLine();
public static int Int => int.Parse(Console.ReadLine());
public static long Long => long.Parse(Console.ReadLine());
public static double Double => double.Parse(Console.ReadLine());
public static T Conv<T>(string input)
{
return (T)Convert.ChangeType(input, typeof(T));
}
public static void Scanf<T>(out T a) => a = Conv<T>(Console.ReadLine());
public static void Scanf<T, U>(out T a, out U b)
{ var q = ReadSplit; a = Conv<T>(q[0]); b = Conv<U>(q[1]); }
public static void Scanf<T, U, V>(out T a, out U b, out V c)
{ var q = ReadSplit; a = Conv<T>(q[0]); b = Conv<U>(q[1]); c = Conv<V>(q[2]); }
public static void Scanf<T, U, V, W>(out T a, out U b, out V c, out W d)
{ var q = ReadSplit; a = Conv<T>(q[0]); b = Conv<U>(q[1]); c = Conv<V>(q[2]); d = Conv<W>(q[3]); }
public static void Scanf<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
{ var q = ReadSplit; a = Conv<T>(q[0]); b = Conv<U>(q[1]); c = Conv<V>(q[2]); d = Conv<W>(q[3]); e = Conv<X>(q[4]); }
}
static class Cout
{
public static void OutL(object s) => Console.WriteLine(s);
public static void Out_Sep<T>(IEnumerable<T> s) => Console.WriteLine(string.Join(" ", s));
public static void Out_Sep<T>(IEnumerable<T> s, string sep) => Console.WriteLine(string.Join($"{sep}", s));
public static void Out_Sep(params object[] s) => Console.WriteLine(string.Join(" ", s));
public static void Out_One(object s) => Console.Write($"{s} ");
public static void Out_One(object s, string sep) => Console.Write($"{s}{sep}");
public static void Endl() => Console.WriteLine();
}
public static class Tool
{
static public void Initialize<T>(ref T[] array, T initialvalue)
{
array = ConvertAll(array, x => initialvalue);
}
static public void Swap<T>(ref T a, ref T b)
{
T keep = a;
a = b;
b = keep;
}
static public void Display<T>(T[,] array2d, int n, int m)
{
for (var i = 0; i < n; i++)
{
for (var j = 0; j < m; j++)
{
Console.Write($"{array2d[i, j]} ");
}
Console.WriteLine();
}
}
static public int GcdI(int a,int b)
{
if (a == 0 || b == 0) return Max(a, b);
return a % b == 0 ? b : GcdI(b, a % b);
}
static public long Gcd(long a, long b)
{
if (a == 0 || b == 0) return Max(a, b);
return a % b == 0 ? b : Gcd(b, a % b);
}
static public long Lcm(long a, long b) => a / Gcd(a, b) * b;
static public int LcmI(int a, int b) => (a == 0 || b == 0) ? Max(a, b) : a / GcdI(a, b) * b;
static public long ExtGcd(long a, long b, ref long x, ref long y)
{
// ax + by = gcd(a,b) なる x,y を求める // return gcd(a,b)
if (b == 0)
{
x = 1; y = 0;
return a;
}
long d = ExtGcd(b, a % b, ref y, ref x);
y -= a / b * x;
return d;
}
static public long LPow(int a, int b) => (long)Pow(a, b);
static public bool Bit(long x, int dig) => ((1L << dig) & x) != 0;
static public int Sig(long a) => a == 0 ? 0 : (int)(a / Abs(a));
static public long F_mp(long x, long n, long mod) => n == 0 ? (1 % mod) : (n % 2 == 0 ? F_mp((x * x) % mod, n >> 1, mod) : (x * F_mp(x, n - 1, mod)) % mod);
static public long F_inv(long x, long mod) => F_mp(x, mod - 2, mod);
static public decimal DSqrt(decimal x, decimal epsilon = 0.0M)
{
if (x < 0) throw new OverflowException("Cannot calculate square root from a negative number");
decimal current = (decimal)Math.Sqrt((double)x), previous;
do
{
previous = current;
if (previous == 0.0M) return 0;
current = (previous + x / previous) / 2;
}
while (Math.Abs(previous - current) > epsilon);
return current;
}
}
public class PrimeList
{
private bool[] isprime;
private List<int> primelist;
public PrimeList(int n)
{
if (n < 2) { return; }
primelist = new List<int>();
isprime = new bool[n + 1];
for (var i = 0; i <= n; i++)
{
isprime[i] = i != 0 && i != 1;
}
for (var i = 2; i <= n; i++)
{
if (!isprime[i]) { continue; }
primelist.Add(i);
int c = i;
while (c + i <= n)
{
c += i;
isprime[c] = false;
}
}
}
public bool IsPrime(int n)
{
return isprime[n];
}
public List<int> GetPrimeList()
{
return primelist;
}
}
static class Permutation<T>
{
private static void Search(List<T[]> perms, Stack<T> stack, T[] a)
{
int N = a.Length;
if (N == 0)
{
perms.Add(stack.Reverse().ToArray());
}
else
{
var b = new T[N - 1];
Array.Copy(a, 1, b, 0, N - 1);
for (int i = 0; i < a.Length; ++i)
{
stack.Push(a[i]);
Search(perms, stack, b);
if (i < b.Length) { b[i] = a[i]; }
stack.Pop();
}
}
}
public static IEnumerable<T[]> All(IEnumerable<T> src)
{
var perms = new List<T[]>();
Search(perms, new Stack<T>(), src.ToArray());
return perms;
}
}
}
namespace AtCoder_MOD
{
public interface IMod
{
int Mod { get; }
// isprime ?
}
public interface INTTFriendly
{
int primitive_root { get; }
}
public readonly struct Mod1000000007 : IMod
{
public int Mod => 1000000007;
}
public readonly struct Mod998244353 : IMod, INTTFriendly
{
public int Mod => 998244353;
public int primitive_root => 3;
}
public struct ModInt<T> where T : IMod
{
private int value;
// 0 <= x < mod 以外でも OK
public ModInt(int x)
{
if (x < 0 || x >= default(T).Mod) x %= default(T).Mod;
if (x < 0) x += default(T).Mod;
value = x;
}
public ModInt(long x)
{
if (x < 0 || x >= default(T).Mod) x %= default(T).Mod;
if (x < 0) x += default(T).Mod;
value = (int)x;
}
// 0 <= x < mod
public ModInt(uint x) => value = (int)x;
public static ModInt<T> operator +(ModInt<T> a, ModInt<T> b)
{
var nv = a.value + b.value;
if (nv >= default(T).Mod) nv -= default(T).Mod;
return new ModInt<T>((uint)nv);
}
public static ModInt<T> operator ++(ModInt<T> a) => a + 1;
public static ModInt<T> operator -(ModInt<T> a, ModInt<T> b)
{
var nv = a.value - b.value;
if (nv < 0) nv += default(T).Mod;
return new ModInt<T>((uint)nv);
}
public static ModInt<T> operator --(ModInt<T> a) => a - 1;
public static ModInt<T> operator *(ModInt<T> a, ModInt<T> b) => new ModInt<T>((uint)(((long)a.value * b.value) % default(T).Mod));
//符号
public static ModInt<T> operator +(ModInt<T> a) => a;
public static ModInt<T> operator -(ModInt<T> a) => a.value == 0 ? a : new ModInt<T>((uint)(default(T).Mod - a.value));
public ModInt<T> Pow(long n)
{
if (n < 0) return Pow(-n).Pow(default(T).Mod - 2);
var p = this;
var ret = new ModInt<T>(1u);
while (n > 0)
{
if ((n & 1) != 0) ret *= p;
p *= p;
n >>= 1;
}
return ret;
}
public ModInt<T> Inverse()
{
Debug.Assert(value != 0);
int x, u, s, t, k;
x = 1; u = 0;
t = default(T).Mod;
s = value;
while (t > 0)
{
k = s / t;
s -= k * t;
(s, t) = (t, s);
x -= k * u;
(x, u) = (u, x);
}
return new ModInt<T>((uint)(x < 0 ? x + default(T).Mod : x));
}
public static ModInt<T> operator /(ModInt<T> a, ModInt<T> b) => (a * b.Inverse());
public static bool operator ==(ModInt<T> a, ModInt<T> b) => a.value == b.value;
public static bool operator !=(ModInt<T> a, ModInt<T> b) => a.value != b.value;
public override bool Equals(object obj) => obj is ModInt<T> && this == (ModInt<T>)obj;
public override int GetHashCode() => value.GetHashCode();
public override string ToString() => value.ToString();
//キャスト
public static implicit operator ModInt<T>(int n) => new ModInt<T>(n);
public static implicit operator ModInt<T>(long n) => new ModInt<T>(n);
public static explicit operator int(ModInt<T> a) => a.value;
public static explicit operator long(ModInt<T> a) => a.value;
public static int GetMod() => default(T).Mod;
}
public static class ModCalc<T> where T : IMod
{
static readonly List<ModInt<T>> fac = new List<ModInt<T>>() { 1 };
static List<ModInt<T>> facinv;
static int MAX_N;
// Do Use Init(Max_n) Before using other functions
public static void Init_Mod(int n)
{
MAX_N = n;
for (int i = 1; i <= n; i++) fac.Add(fac.Last() * i);
facinv = new List<ModInt<T>>() { fac[n].Inverse() };
for (int i = n; i > 0; i--) facinv.Add(facinv.Last() * i);
facinv.Reverse();
}
public static void Reset()
{
MAX_N = -1;
fac.Clear();
facinv.Clear();
}
public static ModInt<T> Fac(int n)
{
Debug.Assert(n <= MAX_N);
return fac[n];
}
public static ModInt<T> Finv(int n)
{
Debug.Assert(n <= MAX_N);
return facinv[n];
}
public static ModInt<T> Binom(int n, int r)
{
Debug.Assert(n <= MAX_N);
if (n < 0 || r < 0 || n < r) return 0;
return fac[n] * facinv[n - r] * facinv[r];
}
public static ModInt<T> ModPow(long x, long n) => new ModInt<T>(x).Pow(n);
public static ModInt<T> ModPow(int x, long n) => new ModInt<T>(x).Pow(n);
public static ModInt<T> ModPow(ModInt<T> x, long n) => x.Pow(n);
public static ModInt<T> Inv(long x) => new ModInt<T>(x).Inverse();
public static ModInt<T> Inv(int x) => new ModInt<T>(x).Inverse();
public static List<ModInt<T>> GetFac() => fac;
public static List<ModInt<T>> GetFacInv() => facinv;
}
public struct MOD_Matrix<T> where T : IMod
{
int n;
ModInt<T>[][] mat;
public MOD_Matrix(int size)
{
n = size;
mat = new ModInt<T>[n][];
for (var i = 0; i < n; i++) mat[i] = new ModInt<T>[n];
}
public MOD_Matrix(int size, ModInt<T>[,] A)
{
n = size;
mat = new ModInt<T>[n][];
for (var i = 0; i < n; i++) mat[i] = new ModInt<T>[n];
for (var i = 0; i < n; i++) for (var j = 0; j < n; j++) mat[i][j] = A[i, j];
}
public MOD_Matrix(int size, ModInt<T>[][] A)
{
n = size;
mat = new ModInt<T>[n][];
for (var i = 0; i < n; i++) mat[i] = new ModInt<T>[n];
for (var i = 0; i < n; i++) for (var j = 0; j < n; j++) mat[i][j] = A[i][j];
}
public MOD_Matrix(int size, long[,] A)
{
n = size;
mat = new ModInt<T>[n][];
for (var i = 0; i < n; i++) mat[i] = new ModInt<T>[n];
for (var i = 0; i < n; i++) for (var j = 0; j < n; j++) mat[i][j] = A[i, j];
}
public MOD_Matrix(int size, long[][] A)
{
n = size;
mat = new ModInt<T>[n][];
for (var i = 0; i < n; i++) mat[i] = new ModInt<T>[n];
for (var i = 0; i < n; i++) for (var j = 0; j < n; j++) mat[i][j] = A[i][j];
}
public MOD_Matrix(int size, int[,] A)
{
n = size;
mat = new ModInt<T>[n][];
for (var i = 0; i < n; i++) mat[i] = new ModInt<T>[n];
for (var i = 0; i < n; i++) for (var j = 0; j < n; j++) mat[i][j] = A[i, j];
}
public MOD_Matrix(int size, int[][] A)
{
n = size;
mat = new ModInt<T>[n][];
for (var i = 0; i < n; i++) mat[i] = new ModInt<T>[n];
for (var i = 0; i < n; i++) for (var j = 0; j < n; j++) mat[i][j] = A[i][j];
}
public ModInt<T>[] this[int id]
{
set
{
Debug.Assert(0 <= id && id < n);
mat[id] = value;
}
get
{
Debug.Assert(0 <= id && id < n);
return mat[id];
}
}
public ModInt<T> this[int id1, int id2]
{
set
{
Debug.Assert(0 <= id1 && id1 < n && 0 <= id2 && id2 < n);
mat[id1][id2] = value;
}
get
{
Debug.Assert(0 <= id1 && id1 < n && 0 <= id2 && id2 < n);
return mat[id1][id2];
}
}
public static MOD_Matrix<T> operator +(MOD_Matrix<T> A, MOD_Matrix<T> B)
{
Debug.Assert(A.n == B.n);
for (var i = 0; i < A.n; i++) for (var j = 0; j < A.n; j++) A[i][j] += B[i][j];
return A;
}
public static MOD_Matrix<T> operator -(MOD_Matrix<T> A, MOD_Matrix<T> B)
{
Debug.Assert(A.n == B.n);
for (var i = 0; i < A.n; i++) for (var j = 0; j < A.n; j++) A[i][j] -= B[i][j];
return A;
}
public static MOD_Matrix<T> operator *(MOD_Matrix<T> A, MOD_Matrix<T> B)
{
Debug.Assert(A.n == B.n);
var ret = new MOD_Matrix<T>(A.n);
for (var i = 0; i < A.n; i++) for (var j = 0; j < A.n; j++)
{
for (var k = 0; k < A.n; k++) ret[i][j] += A[i][k] * B[k][j];
}
return ret;
}
public static ModInt<T>[] operator *(MOD_Matrix<T> A, ModInt<T>[] V)
{
Debug.Assert(A.n == V.Length);
var ret = new ModInt<T>[A.n];
for (var i = 0; i < A.n; i++)
{
for (var j = 0; j < A.n; j++) ret[i] += A[i][j] * V[j];
}
return ret;
}
public static MOD_Matrix<T> operator *(MOD_Matrix<T> A, ModInt<T> k)
{
for (var i = 0; i < A.n; i++) for (var j = 0; j < A.n; j++) A[i][j] *= k;
return A;
}
public MOD_Matrix<T> Pow(long K)
{
Debug.Assert(K >= 0);
if (K == 0)
{
var E = new MOD_Matrix<T>(n);
for (var i = 0; i < n; i++) E[i][i] = 1;
return E;
}
var ret = new MOD_Matrix<T>(n);
var P = this;
for (var i = 0; i < n; i++) ret[i][i] = 1;
while (K > 0)
{
if ((K & 1) != 0) ret *= P;
P *= P; K >>= 1;
}
return ret;
}
public static ModInt<T> Solve_Linear_dp(long N, ModInt<T>[] coefs, ModInt<T>[] inits)
{
int K = coefs.Length;
if (N < K) return inits[K - 1 - N];
var A = new MOD_Matrix<T>(K);
for (var i = 0; i < K; i++)
{
if (i == 0) for (var j = 0; j < K; j++) A[i][j] = coefs[j];
else A[i][i - 1] = 1;
}
N -= K - 1;
A = A.Pow(N);
inits = A * inits;
return inits[0];
}
}
public class MOD_NTT<T> where T : IMod, INTTFriendly
{
private readonly int mod;
private readonly int root;
public MOD_NTT()
{
mod = default(T).Mod;
root = default(T).primitive_root;
}
void NTT(ref ModInt<T>[] a, bool rev = false)
{
var n = a.Length;
if (n == 1) return;
var b = new ModInt<T>[n];
var s = new ModInt<T>(root).Pow(rev ? mod - 1 - (mod - 1) / n : (mod - 1) / n);
var kp = new List<ModInt<T>>() { 1 };
int i, j, k, l, r;
for (i = 0; i < (n >> 1); ++i) kp.Add(kp.Last() * s);
for (i = 1, l = (n >> 1); i < n; i <<= 1, l >>= 1)
{
for (j = 0, r = 0; j < l; ++j, r += i)
{
for (k = 0, s = kp[i * j]; k < i; ++k)
{
var p = a[k + r]; var q = a[k + r + n / 2];
b[k + 2 * r] = (p + q);
b[k + 2 * r + i] = ((p - q) * s);
}
}
(a, b) = (b, a);
}
if (rev)
{
s = new ModInt<T>(n).Inverse();
for (i = 0; i < n; ++i) a[i] *= s;
}
}
public ModInt<T>[] Convolution_MOD(ModInt<T>[] a, ModInt<T>[] b)
{
int N = a.Length + b.Length - 1;
int t = 1;
while (t < N) t <<= 1;
var nxa = new ModInt<T>[t];
var nxb = new ModInt<T>[t];
for (var i = 0; i < a.Length; ++i) nxa[i] = a[i];
for (var i = 0; i < b.Length; ++i) nxb[i] = b[i];
NTT(ref nxa);
NTT(ref nxb);
for (var i = 0; i < t; i++) nxa[i] *= nxb[i];
NTT(ref nxa, true);
return nxa[0..N];
}
public ModInt<T>[] Convolution_MOD(long[] a, long[] b)
{
int N = a.Length + b.Length - 1;
int t = 1;
while (t < N) t <<= 1;
var nxa = new ModInt<T>[t];
var nxb = new ModInt<T>[t];
for (var i = 0; i < a.Length; ++i) nxa[i] = a[i];
for (var i = 0; i < b.Length; ++i) nxb[i] = b[i];
NTT(ref nxa);
NTT(ref nxb);
for (var i = 0; i < t; i++) nxa[i] *= nxb[i];
NTT(ref nxa, true);
return nxa[0..N];
}
}
//次数固定、NTT対応modのみ
public struct FormalPowerSeries<T> where T : IMod, INTTFriendly
{
int n;
ModInt<T>[] P;
static readonly MOD_NTT<T> C = new MOD_NTT<T>();
public FormalPowerSeries(int n)
{
this.n = n;
P = new ModInt<T>[n + 1];
}
public int Length => n;
public ModInt<T> this[int id]
{
set
{
Debug.Assert(0 <= id && id <= n);
P[id] = value;
}
get
{
Debug.Assert(0 <= id && id <= n);
return P[id];
}
}
//Add
//O(min(n,m))
public static FormalPowerSeries<T> operator +(FormalPowerSeries<T> F, FormalPowerSeries<T> G)
{
int m = Math.Min(F.Length, G.Length);
for (var i = 0; i <= m; i++) F[i] += G[i];
return F;
}
//O(1)
public static FormalPowerSeries<T> operator +(FormalPowerSeries<T> F, ModInt<T> a)
{
F[0] += a;
return F;
}
//Subtract
//O(min(n,m))
public static FormalPowerSeries<T> operator -(FormalPowerSeries<T> F, FormalPowerSeries<T> G)
{
int m = Math.Min(F.Length, G.Length);
for (var i = 0; i <= m; i++) F[i] -= G[i];
return F;
}
//O(1)
public static FormalPowerSeries<T> operator -(FormalPowerSeries<T> F, ModInt<T> a)
{
F[0] -= a;
return F;
}
// Multiply
//O(nlog(n))
//下位 n 項のみ残すことに注意
public static FormalPowerSeries<T> operator *(FormalPowerSeries<T> F, FormalPowerSeries<T> G)
{
F.P = C.Convolution_MOD(F.P, G.P)[0..(F.n + 1)];
return F;
}
//O(n)
public static FormalPowerSeries<T> operator *(FormalPowerSeries<T> F, ModInt<T> a)
{
for (var i = 0; i <= F.n; i++) F[i] *= a;
return F;
}
//Divide
//Todo F/=G
//O(n+log(mod))
public static FormalPowerSeries<T> operator /(FormalPowerSeries<T> F, ModInt<T> a)
{
var inv = a.Inverse();
for (var i = 0; i <= F.n; i++) F[i] *= inv;
return F;
}
}
}