using System; using System.Collections.Generic; using System.Linq; using System.IO; using System.Text; using System.Numerics; using System.Threading; using System.Runtime.InteropServices; 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 static AtCoder.StringTools; //using ModInt = AtCoder_MOD.ModInt;using static AtCoder_MOD.ModCalc;using MOD_Matrix = AtCoder_MOD.MOD_Matrix; using ModInt = AtCoder_MOD.ModInt;using static AtCoder_MOD.ModCalc;using MOD_Matrix = AtCoder_MOD.MOD_Matrix; using Bint = System.Numerics.BigInteger; 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 M, out int K); var X = Cin.Str; var dp = new ModInt[M + 1][]; for (var i = 0; i <= M; i++) dp[i] = new ModInt[N + 1]; var mp = new ModInt[N + 1]; mp[0] = 1; for (var i = 1; i <= N; i++) mp[i] = (mp[i - 1] * 2); dp[0][N] = 1; Init_Mod(N + 1); for(var i = 0; i < M; i++) { if (X[i] == '0') { for(var j = K; j <= N; j++) { for(var k = K; k <= j; k++) { dp[i + 1][k] += dp[i][j] * Binom(j, k) * mp[N - j]; } } } else { for(var j = K; j <= N; j++) { for(var z = 0; z < K; z++) { dp[i + 1][j] += dp[i][j] * Binom(j, z) * mp[N - j]; } } } } ModInt ans = 0; for (var i = K; i <= N; i++) ans += dp[M][i]; OutL(ans); } struct E { public int to; public long w; public E(int _to,long _w) { to = _to;w = _w; } } } 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 { public int H, W; public T[] mat; public static T Ip { set; get; } public static T Im { set; get; } public static Func fp { set; get; } public static Func 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 FP, T IP, Func 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 operator +(Matrix m1, Matrix 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 operator *(Matrix m1, Matrix m2) { Debug.Assert(m1.W == m2.H); var ret = new Matrix(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 Pow(long K) { Debug.Assert(H == W); int n = H; Debug.Assert(K >= 0); var ret = new Matrix(n, n); for (var i = 0; i < n; i++) ret[i, i] = Im; if (K == 0) return ret; var P = new Matrix(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> Gen_Graph(int size) { var ret = new List>(); for (var i = 0; i < size; i++) ret.Add(new List()); return ret; } public static long[] Dijkstra(List> G, int st) { int N = G.Count(); long[] ret = new long[N]; var V = new Priority_Queue>((x, y) => Sgn(x.Item1 - y.Item1)); for (var i = 0; i < N; i++) ret[i] = inf; ret[st] = 0; V.Enqueue(new Tuple(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(ret[ed.to], ed.to)); } } } return ret; } public static long[] Bellman_Frod(List 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 E; int[] id; public SCC(int size) { n = size; E = new List(); } 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>(); 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(); for (var i = 0; i < n; i++) ord[i] = -1; int nowid = 0; Action 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()); 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> G; int[] level, itr; public Dinic(int vertice) { n = vertice; level = new int[n]; itr = new int[n]; G = new List>(); for (var _ = 0; _ < n; _++) G.Add(new List()); } //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(); 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> 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> G; public MinCostFlow(int size) { n = size; G = new List>(); for (var i = 0; i < n; i++) G.Add(new List()); } /*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) => Sgn(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> GetEdges() => G; } public class LCA { List> G1; List> G2; int n; bool isweighted; int[] dist; long[] dist_w; int[,] par; public LCA(List> 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> 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(); 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 { private List Q; private readonly Comparison Func_Compare; public Priority_Queue(Comparison comp) { Func_Compare = comp; Q = new List(); } 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 { //1-indexed type int n; T[] Tree; Func f; T ex; int len; [MethodImpl(MethodImplOptions.AggressiveInlining)] public SegmentTree(int size, Func 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 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 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 { int n, L; X[] Tree; A[] lazy; Func fxx; Func faa; Func fxa; X exx; A exa; public LazySegmentTree(int size, Func funcxx, Func funcaa, Func 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 static int[] MP_Build(string T) { var ret = new int[T.Length + 1]; int j = -1; ret[0] = -1; for (var i = 0; i < T.Length; i++) { while (j >= 0 && T[i] != T[j]) j = ret[j]; j++; ret[i + 1] = j; } return ret; } public static int MP_Match(string S, string T, int[] MP_table) { int ids = 0, idt = 0; while (ids < S.Length && idt < T.Length) { if (S[ids] == T[idt]) { ids++; idt++; } else { idt = MP_table[idt]; if (idt == -1) { idt = 0; ids++; } } } return idt == T.Length ? ids - T.Length : -1; } public static int[] Manachar(string S) { int i = 0, j = 0; var ret = new int[S.Length]; while (i < S.Length) { while (i - j >= 0 && i + j < S.Length && S[i - j] == S[i + j]) j++; ret[i] = j; int k = 1; while (i - k >= 0 && k + ret[i - k] < j) { ret[i + k] = ret[i - 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 n; private int[] par_size; // par_size[i] = sizeof(i) (par_size[i] < 0) // parent(i) (par_size[i] >= 0) public UnionFind(int size) { n = size; par_size = new int[n]; for (var i = 0; i < n; i++) par_size[i] = -1; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public int Root(int v) { if (par_size[v] < 0) return v; while (par_size[par_size[v]] >= 0) { (v, par_size[v]) = (par_size[v], par_size[par_size[v]]); } return par_size[v]; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public int SizeOf(int v) => -par_size[Root(v)]; public void Unite(int u, int v) { int ru = Root(u), rv = Root(v); if (ru == rv) return; if (par_size[ru] > par_size[rv]) { par_size[rv] += par_size[ru]; par_size[ru] = rv; } else { par_size[ru] += par_size[rv]; par_size[rv] = ru; } } [MethodImpl(MethodImplOptions.AggressiveInlining)] public bool Same(int u, int v) => Root(u) == Root(v); } public class Deque { T[] buf; int offset, count, capacity; public int Count { get { return count; } } public Deque(int cap) { buf = new T[capacity = cap]; } public Deque() { buf = new T[capacity = 16]; } public T this[int index] { get { return buf[getIndex(index)]; } set { buf[getIndex(index)] = value; } } private int getIndex(int index) { if (index >= capacity) throw new IndexOutOfRangeException("out of range"); var ret = index + offset; if (ret >= capacity) ret -= capacity; return ret; } public void PushFront(T item) { if (count == capacity) Extend(); if (--offset < 0) offset += buf.Length; buf[offset] = item; ++count; } public T PopFront() { if (count == 0) throw new InvalidOperationException("collection is empty"); --count; var ret = buf[offset++]; if (offset >= capacity) offset -= capacity; return ret; } public void PushBack(T item) { if (count == capacity) Extend(); var id = count++ + offset; if (id >= capacity) id -= capacity; buf[id] = item; } public T PopBack() { if (count == 0) throw new InvalidOperationException("collection is empty"); return buf[getIndex(--count)]; } public void Insert(int index, T item) { if (index > count) throw new IndexOutOfRangeException(); this.PushFront(item); for (int i = 0; i < index; i++) this[i] = this[i + 1]; this[index] = item; } public T RemoveAt(int index) { if (index < 0 || index >= count) throw new IndexOutOfRangeException(); var ret = this[index]; for (int i = index; i > 0; i--) this[i] = this[i - 1]; this.PopFront(); return ret; } private void Extend() { T[] newBuffer = new T[capacity << 1]; if (offset > capacity - count) { var len = buf.Length - offset; Array.Copy(buf, offset, newBuffer, 0, len); Array.Copy(buf, 0, newBuffer, len, count - len); } else Array.Copy(buf, offset, newBuffer, 0, count); buf = newBuffer; offset = 0; capacity <<= 1; } public T[] Items//デバッグ時に中身を調べるためのプロパティ { get { var a = new T[count]; for (int i = 0; i < count; i++) a[i] = this[i]; return a; } } } 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(string input) { return (T)Convert.ChangeType(input, typeof(T)); } public static void Scanf(out T a) => a = Conv(Console.ReadLine()); public static void Scanf(out T a, out U b) { var q = ReadSplit; a = Conv(q[0]); b = Conv(q[1]); } public static void Scanf(out T a, out U b, out V c) { var q = ReadSplit; a = Conv(q[0]); b = Conv(q[1]); c = Conv(q[2]); } public static void Scanf(out T a, out U b, out V c, out W d) { var q = ReadSplit; a = Conv(q[0]); b = Conv(q[1]); c = Conv(q[2]); d = Conv(q[3]); } public static void Scanf(out T a, out U b, out V c, out W d, out X e) { var q = ReadSplit; a = Conv(q[0]); b = Conv(q[1]); c = Conv(q[2]); d = Conv(q[3]); e = Conv(q[4]); } } static class Cout { public static void OutL(object s) => Console.WriteLine(s); public static void Out_Sep(IEnumerable s) => Console.WriteLine(string.Join(" ", s)); public static void Out_Sep(IEnumerable 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(ref T[] array, T initialvalue) { array = ConvertAll(array, x => initialvalue); } static public void Swap(ref T a, ref T b) { T keep = a; a = b; b = keep; } static public void Display(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 Sgn(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 primelist; public PrimeList(int n) { if (n < 2) { return; } primelist = new List(); 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 GetPrimeList() { return primelist; } } static class Permutation { private static void Search(List perms, Stack 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 All(IEnumerable src) { var perms = new List(); Search(perms, new Stack(), 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 readonly struct Mod1000000006 : IMod { public int Mod => 1000000006; } public readonly struct Mod10 : IMod { public int Mod => 10; } public struct ModInt where T : IMod { private readonly int value; public ModInt(int x) => value = x; public ModInt(long x) { x %= default(T).Mod; if (x < 0) x += default(T).Mod; value = (int)x; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt operator +(ModInt a, ModInt b) { var nv = a.value + b.value; if (nv >= default(T).Mod) nv -= default(T).Mod; return new ModInt(nv); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt operator ++(ModInt a) => a + 1; [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt operator -(ModInt a, ModInt b) { var nv = a.value - b.value; if (nv < 0) nv += default(T).Mod; return new ModInt(nv); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt operator --(ModInt a) => a - 1; [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt operator *(ModInt a, ModInt b) => new ModInt((int)((long)a.value * b.value % default(T).Mod)); //符号 [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt operator +(ModInt a) => a; [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt operator -(ModInt a) => a.value == 0 ? a : new ModInt((default(T).Mod - a.value)); public ModInt Pow(long n) { if (n < 0) return Pow(-n).Pow(default(T).Mod - 2); var p = this; var ret = new ModInt(1); while (n > 0) { if ((n & 1) != 0) ret *= p; p *= p; n >>= 1; } return ret; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public ModInt 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((x < 0 ? x + default(T).Mod : x)); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt operator /(ModInt a, ModInt b) => (a * b.Inverse()); public static bool operator ==(ModInt a, ModInt b) => a.value == b.value; public static bool operator !=(ModInt a, ModInt b) => a.value != b.value; public override bool Equals(object obj) => obj is ModInt && this == (ModInt)obj; public override int GetHashCode() => value.GetHashCode(); public override string ToString() => value.ToString(); //キャスト public static implicit operator ModInt(int n) => new ModInt(n); public static implicit operator ModInt(long n) => new ModInt(n); public static explicit operator int(ModInt a) => a.value; public static explicit operator long(ModInt a) => a.value; public static int GetMod() => default(T).Mod; } public static class ModCalc where T : IMod { static readonly List> fac = new List>() { 1 }; static List> 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>() { 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 Fac(int n) { Debug.Assert(n <= MAX_N); return fac[n]; } public static ModInt Finv(int n) { Debug.Assert(n <= MAX_N); return facinv[n]; } public static ModInt 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 ModPow(long x, long n) => new ModInt(x).Pow(n); public static ModInt ModPow(int x, long n) => new ModInt(x).Pow(n); public static ModInt ModPow(ModInt x, long n) => x.Pow(n); public static ModInt Inv(long x) => new ModInt(x).Inverse(); public static ModInt Inv(int x) => new ModInt(x).Inverse(); public static List> GetFac() => fac; public static List> GetFacInv() => facinv; } public struct MOD_Matrix where T : IMod { int n; ModInt[][] mat; public MOD_Matrix(int size) { n = size; mat = new ModInt[n][]; for (var i = 0; i < n; i++) mat[i] = new ModInt[n]; } public MOD_Matrix(int size, ModInt[,] A) { n = size; mat = new ModInt[n][]; for (var i = 0; i < n; i++) mat[i] = new ModInt[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[][] A) { n = size; mat = new ModInt[n][]; for (var i = 0; i < n; i++) mat[i] = new ModInt[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[n][]; for (var i = 0; i < n; i++) mat[i] = new ModInt[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[n][]; for (var i = 0; i < n; i++) mat[i] = new ModInt[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[n][]; for (var i = 0; i < n; i++) mat[i] = new ModInt[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[n][]; for (var i = 0; i < n; i++) mat[i] = new ModInt[n]; for (var i = 0; i < n; i++) for (var j = 0; j < n; j++) mat[i][j] = A[i][j]; } public ModInt[] 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 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 operator +(MOD_Matrix A, MOD_Matrix 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 operator -(MOD_Matrix A, MOD_Matrix 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 operator *(MOD_Matrix A, MOD_Matrix B) { Debug.Assert(A.n == B.n); var ret = new MOD_Matrix(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[] operator *(MOD_Matrix A, ModInt[] V) { Debug.Assert(A.n == V.Length); var ret = new ModInt[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 operator *(MOD_Matrix A, ModInt 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 Pow(long K) { Debug.Assert(K >= 0); if (K == 0) { var E = new MOD_Matrix(n); for (var i = 0; i < n; i++) E[i][i] = 1; return E; } var ret = new MOD_Matrix(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 Solve_Linear_dp(long N, ModInt[] coefs, ModInt[] inits) { int K = coefs.Length; if (N < K) return inits[K - 1 - N]; var A = new MOD_Matrix(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 where T : IMod, INTTFriendly { private readonly int M, root; public MOD_NTT() { M = default(T).Mod; root = default(T).primitive_root; } public Span> Convolution_MOD(ReadOnlySpan a, ReadOnlySpan b) { var aa = new ModInt[a.Length]; var bb = new ModInt[b.Length]; for (var i = 0; i < a.Length; i++) aa[i] = a[i]; for (var i = 0; i < b.Length; i++) bb[i] = b[i]; return Convolution_MOD(aa.AsSpan(), bb.AsSpan()); } public Span> Convolution_MOD(ReadOnlySpan a, ReadOnlySpan b) { var aa = new ModInt[a.Length]; var bb = new ModInt[b.Length]; for (var i = 0; i < a.Length; i++) aa[i] = a[i]; for (var i = 0; i < b.Length; i++) bb[i] = b[i]; return Convolution_MOD(aa.AsSpan(), bb.AsSpan()); } public Span> Convolution_MOD(ReadOnlySpan> a, ReadOnlySpan> b) { int len = a.Length + b.Length - 1; int n = 1; while (len > n) n <<= 1; var sa = new ModInt[n]; var sb = new ModInt[n]; a.CopyTo(sa); b.CopyTo(sb); var resa = NTT(sa); var resb = NTT(sb); for (var i = 0; i < n; i++) resa[i] *= resb[i]; var ret = NTT(resa, true); return ret.Slice(0, len); } Span> NTT(Span> x, bool Inv = false) { var n = x.Length; if (n == 1) return x; var y = new ModInt[n].AsSpan(); var s = new ModInt(root).Pow(Inv ? M - 1 - (M - 1) / n : (M - 1) / n); var kp = new ModInt[(n >> 1) + 1]; kp[0] = 1; int i, j, k, l, r; var mod_v = new Vector(default(T).Mod); var zero_v = new Vector(0); int L = Vector.Count; for (i = 0; i < (n >> 1); ++i) kp[i + 1] = kp[i] * s; for (i = 1, l = (n >> 1); i < n; i <<= 1, l >>= 1) { for (j = 0, r = 0; j < l; ++j, r += i) { if (i < L) { for (k = 0, s = kp[i * j]; k < i; ++k) { var p = x[k + r]; var q = x[k + r + (n >> 1)]; y[k + (r << 1)] = (p + q); y[k + (r << 1) + i] = ((p - q) * s); } } else { s = kp[i * j]; var lu = MemoryMarshal.Cast, int>(x.Slice(r, i)); var ru = MemoryMarshal.Cast, int>(x.Slice(r + (n >> 1), i)); var buf = new int[L << 1]; var yl = MemoryMarshal.Cast, int>(y.Slice(r << 1, i)); var yr = MemoryMarshal.Cast, int>(y.Slice((r << 1) + i, i)); for (int st = 0; st < i; st += L) { var lu_slice = lu.Slice(st); var ru_slice = ru.Slice(st); var add = new Vector(lu_slice); var v = new Vector(ru_slice); for (k = 0; k < L; ++k) { buf[k] = (int)(s * add[k]); buf[L + k] = (int)(s * v[k]); } var sub = new Vector(buf.AsSpan().Slice(0, L)); var vs = new Vector(buf.AsSpan().Slice(L, L)); //var add = u + v; add += v; //var sub = us - vs; sub -= vs; var flag = Vector.GreaterThanOrEqual(add, mod_v); add = Vector.ConditionalSelect(flag, add - mod_v, add); flag = Vector.LessThan(sub, zero_v); sub = Vector.ConditionalSelect(flag, sub + mod_v, sub); add.CopyTo(yl.Slice(st, L)); sub.CopyTo(yr.Slice(st, L)); } } } var kep = x; x = y; y = kep; } if (Inv) { s = new ModInt(n).Inverse(); for (i = 0; i < n; ++i) x[i] *= s; } return x; } } }