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【题目链接】
【思路要点】
【代码】
#include<bits/stdc++.h> using namespace std; const int MAXN = 64; const int MAXM = 65536; const int P = 998244353; typedef long long ll; typedef long double ld; typedef unsigned long long ull; template <typename T> void chkmax(T &x, T y) {x = max(x, y); } template <typename T> void chkmin(T &x, T y) {x = min(x, y); } template <typename T> void read(T &x) { x = 0; int f = 1; char c = getchar(); for (; !isdigit(c); c = getchar()) if (c == '-') f = -f; for (; isdigit(c); c = getchar()) x = x * 10 + c - '0'; x *= f; } template <typename T> void write(T x) { if (x < 0) x = -x, putchar('-'); if (x > 9) write(x / 10); putchar(x % 10 + '0'); } template <typename T> void writeln(T x) { write(x); puts(""); } namespace BerlekampMassey { const int MAXN = 205; const int P = 998244353; int cnt, fail[MAXN], delta[MAXN]; vector <int> ans[MAXN]; int power(int x, int y) { if (y == 0) return 1; int tmp = power(x, y / 2); if (y % 2 == 0) return 1ll * tmp * tmp % P; else return 1ll * tmp * tmp % P * x % P; } vector <int> work(int n, int *val) { ans[cnt = 0].clear(); for (int i = 1; i <= n; i++) { int now = val[i]; for (unsigned j = 0; j < ans[cnt].size(); j++) now = (now - 1ll * val[i - j - 1] * ans[cnt][j] % P + P) % P; delta[i] = now; if (now == 0) continue; fail[cnt] = i; if (cnt == 0) { ans[++cnt].clear(); ans[cnt].resize(i); continue; } ans[++cnt].clear(); ans[cnt].resize(i - fail[cnt - 2] - 1); int mul = 1ll * now * power(delta[fail[cnt - 2]], P - 2) % P; ans[cnt].push_back(mul); for (unsigned j = 0; j < ans[cnt - 2].size(); j++) ans[cnt].push_back(1ll * ans[cnt - 2][j] * (P - mul) % P); if (ans[cnt].size() < ans[cnt - 1].size()) ans[cnt].resize(ans[cnt - 1].size()); for (unsigned j = 0; j < ans[cnt - 1].size(); j++) ans[cnt][j] = (ans[cnt][j] + ans[cnt - 1][j]) % P; } //cerr << ans[cnt].size() << endl; return ans[cnt]; } } namespace NTT { const int MAXN = 65536; const int P = 998244353; const int G = 3; int power(int x, int y) { if (y == 0) return 1; int tmp = power(x, y / 2); if (y % 2 == 0) return 1ll * tmp * tmp % P; else return 1ll * tmp * tmp % P * x % P; } int N, Log, home[MAXN]; void NTTinit() { for (int i = 0; i < N; i++) { int ans = 0, tmp = i; for (int j = 1; j <= Log; j++) { ans <<= 1; ans += tmp & 1; tmp >>= 1; } home[i] = ans; } } void NTT(int *a, int mode) { for (int i = 0; i < N; i++) if (home[i] < i) swap(a[i], a[home[i]]); for (int len = 2; len <= N; len <<= 1) { int delta; if (mode == 1) delta = power(G, (P - 1) / len); else delta = power(G, P - 1 - (P - 1) / len); for (int i = 0; i < N; i += len) { int now = 1; for (int j = i, k = i + len / 2; k < i + len; j++, k++) { int tmp = a[j]; int tnp = 1ll * a[k] * now % P; a[j] = (tmp + tnp) % P; a[k] = (tmp - tnp + P) % P; now = 1ll * now * delta % P; } } } if (mode == -1) { int inv = power(N, P - 2); for (int i = 0; i < N; i++) a[i] = 1ll * a[i] * inv % P; } } void times(int *a, int *b, int *c, int limit) { N = 1, Log = 0; while (N < 2 * limit) { N <<= 1; Log++; } for (int i = limit; i < N; i++) a[i] = b[i] = 0; NTTinit(); NTT(a, 1); NTT(b, 1); for (int i = 0; i < N; i++) c[i] = 1ll * a[i] * b[i] % P; NTT(c, -1); } void timesabb(int *a, int *b, int *c, int limit) { N = 1, Log = 0; while (N < 2 * limit) { N <<= 1; Log++; } for (int i = limit; i < N; i++) a[i] = 0; for (int i = limit / 2; i < N; i++) b[i] = 0; NTTinit(); NTT(a, 1); NTT(b, 1); for (int i = 0; i < N; i++) c[i] = 1ll * a[i] * b[i] % P * b[i] % P; NTT(c, -1); } void inverse(int *a, int *b, int limit) { for (int i = 0; i < 2 * limit; i++) { if (i >= limit) a[i] = 0; b[i] = 0; } b[0] = power(a[0], P - 2); for (int now = 1; now < limit; now <<= 1) { static int c[MAXN], d[MAXN]; for (int i = 0; i < now * 2; i++) c[i] = a[i], d[i] = b[i]; timesabb(c, d, d, now * 2); for (int i = 0; i < now * 2; i++) b[i] = (2ll * b[i] - d[i] + P) % P; } } } int n, m; int mat[MAXN][MAXN]; int res[MAXN][MAXM]; int inv[MAXN][MAXM]; void update(int &x, int y) { x += y; if (x >= P) x -= P; } int main() { read(n), read(m); for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) read(mat[i][j]); static int ways[MAXN * 2 + 15][MAXN][MAXN]; for (int i = 0; i < n; i++) ways[0][i][i] = 1; int steps = n * 2 + 5; for (int t = 1; t <= steps; t++) { for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) for (int k = 0; k < n; k++) update(ways[t][i][k], 1ll * ways[t - 1][i][j] * mat[j][k] % P); for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) update(res[i & j][t], ways[t][i][j]); } static int tmp[MAXN * 2 + 15]; for (int t = 1; t <= steps; t++) { int tres = 0; for (int i = 0; i < n; i++) tres = (13331ll * tres + res[i][t]) % P; tmp[t] = tres; } vector <int> h = BerlekampMassey :: work(steps, tmp); for (int i = 0; i < n; i++) { for (int t = steps + 1; t <= m; t++) { int tres = 0; for (unsigned j = 0; j < h.size(); j++) update(tres, 1ll * res[i][t - j - 1] * h[j] % P); res[i][t] = tres; } } for (int i = 0; i < n; i++) { for (int t = 1; t <= m; t++) for (int j = i + 1; j < n; j++) if ((i | j) == j) update(res[i][t], res[j][t]); res[i][0] = 1; for (int j = 1; j <= m; j++) res[i][j] = P - res[i][j]; NTT :: inverse(res[i], inv[i], m + 1); } int ans = 0; for (int t = 1; t <= m; t++) { for (int i = n - 1; i >= 0; i--) { for (int j = i + 1; j < n; j++) if ((i | j) == j) update(inv[i][t], P - inv[j][t]); ans ^= inv[i][t]; } } writeln(ans); return 0; }