#define ATCODER #define _USE_MATH_DEFINES #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using ld = long double; using pll = pair; using pdd = pair; //template using pq = priority_queue, greater>; #define FOR(i, a, b) for(ll i=(a); i<(b);i++) #define REP(i, n) for(ll i=0; i<(n);i++) #define ROF(i, a, b) for(ll i=(b-1); i>=(a);i--) #define PER(i, n) for(ll i=n-1; i>=0;i--) #define REPREP(i,j,a,b) for(ll i=0;i > #define VV2(type,n,m,val) vector< vector > val;val.resize(n);for(ll i;i #define VEC(type,n,val) vector val;val.resize(n) #define VL vector #define VVL vector< vector > #define VP vector< pair > #define SZ size() #define all(i) begin(i),end(i) #define SORT(i) sort(all(i)) #define BITI(i) (1<>i) & 1) != 0) #define ALLBIT(n) (ll(1)<v?v:n #define MP(a,b) make_pair(a,b) #define DET2(x1,y1,x2,y2) (x1)*(y2)-(x2)*(y1) #define DET3(x1,y1,z1,x2,y2,z2,x3,y3,z3) (x1)*(y2)*(z3)+(x2)*(y3)*(z1)+(x3)*(y1)*(z2)-(z1)*(y2)*(x3)-(z2)*(y3)*(x1)-(z3)*(y1)*(x2) #define INC(a) for(auto& v:a)v++; #define DEC(a) for(auto& v:a)v--; #define SQU(x) (x)*(x) #define L0 ll(0) #ifdef ATCODER #include using namespace atcoder; using mint = modint1000000007; using mint2 = modint998244353; #endif template vector read(size_t n) { vector ts(n); for (size_t i = 0; i < n; i++) cin >> ts[i]; return ts; } template void read_tuple_impl(TV&) {} template void read_tuple_impl(TV& ts) { get(ts).emplace_back(*(istream_iterator(cin))); read_tuple_impl(ts); } template decltype(auto) read_tuple(size_t n) { tuple...> ts; for (size_t i = 0; i < n; i++) read_tuple_impl(ts); return ts; } using val = ll; //using func = pair; val op(val a, val b) { return min(a, b); } val e() { return 1e18; } using val2 = mint2; //using func = pair; val2 op2(val2 a, val2 b) { return a * b; } val2 e2() { return 1; } // //val mp(func f, val a) //{ // if (f.first < 0) // return a; // return f; //} //func comp(func f, func g) { // if (g.first < 0) // return f; // return g; //} // //func id() { // return MP(-1, -1); //} ll di[4] = { 1,0,-1,0 }; ll dj[4] = { 0,1,0,-1 }; ll si[4] = { 0,3,3,0 }; ll sj[4] = { 0,0,3,3 }; //ll di[4] = { -1,-1,1,1 }; //ll dj[4] = { -1,1,-1,1 }; ll di8[8] = { 0,-1,-1,-1,0,1,1,1 }; ll dj8[8] = { -1,-1,0,1,1,1,0,-1 }; class NimberManager { private: using u32 = unsigned int; using u64 = unsigned long long; std::vector precalc1; std::vector inv_precalc1; void fill_precalc1() { precalc1.assign(1 << 16, 0); precalc1[(1 << 8) ^ 1] = 1; for (int dd = 1; dd < 8; dd <<= 1) { int d = 1 << dd; int c = d >> 1; for (int a0 = 0; a0 < d; a0++) for (int a1 = 0; a1 < d; a1++) if (a0 | a1) { for (int b0 = 0; b0 < d; b0++) for (int b1 = 0; b1 < d; b1++) if (b0 | b1) { u64 buf = 0; buf ^= precalc1[(a1 << 8) ^ b1]; buf ^= precalc1[(a1 << 8) ^ b0]; buf ^= precalc1[(a0 << 8) ^ b1]; buf <<= dd; buf ^= precalc1[(c << 8) ^ precalc1[(a1 << 8) ^ b1]]; buf ^= precalc1[(a0 << 8) ^ b0]; precalc1[(((a1 << dd) ^ a0) << 8) ^ ((b1 << dd) ^ b0)] = buf; } } } } void inv_precalc() { inv_precalc1.resize(256); for (int i = 0; i < 256; ++i) { for (int j = 0; j < 256; ++j) { if (precalc1[(i << 8) ^ j] == 1) { inv_precalc1[i] = j; break; } } } } u64 product_full(u64 a, u64 b, int d = 6) noexcept { if (!(a && b)) return 0; if (d == 3) { return precalc1[(a << 8) ^ b]; } d--; u64 lm = ((u64)1 << (1 << d)) - 1; u64 us = ((u64)1 << d); u64 buf = 0; u64 a1b1 = product_full(a >> us, b >> us, d); u64 a2b2 = product_full(a & lm, b & lm, d); u64 aabb = product_full((a & lm) ^ (a >> us), (b & lm) ^ (b >> us), d); buf ^= (aabb ^ a2b2); buf <<= us; buf ^= a2b2; buf ^= product_full((u64)1 << (us - 1), a1b1, d); return buf; } u64 inv_full(u64 a, int d = 6) { if (a < 256) { return inv_precalc1[a]; } u64 p = 1 << (d - 1); u64 a_h = a >> p; u64 a_l = a - (a_h << p); u64 half_inv = inv_full(product_full(a_h ^ a_l, a_l, d) ^ product_full(product_full(a_h, a_h, d - 1), 1ULL << (p - 1)), d - 1); return (product_full(half_inv, a_h, d) << p) ^ product_full(half_inv, a_h ^ a_l, d); return (product_full(half_inv, a_h, d) << p) ^ product_full(half_inv, a_h ^ a_l, d); } public: NimberManager() { fill_precalc1(); inv_precalc(); } unsigned long long product(unsigned long long a, unsigned long long b) noexcept { return product_full(a, b); } unsigned long long pow(unsigned long long a, unsigned long long idx) noexcept { if (idx == 0) return 1; auto b = pow(product(a, a), idx / 2); if (idx & 1) b = product(b, a); return b; } unsigned long long inv(unsigned long long a) noexcept { return inv_full(a); } }; void solve() { NimberManager nm; ll n, t; cin >> n >> t; vector h(t, vector()); REP(i, t) { h[i] = read(n); DEC(h[i]); } mint2 fr = mint2(2).pow(64); mint2 frinv = fr.inv(); vector col(n, -1); vector raw(t, -1); mint2 ans = 0; mint2 add = 1; REP(j, n) { unsigned long long inv = 0; REP(i, t) { if (raw[i] != -1 || h[i][j] == 0) continue; col[j] = i; raw[i] = j; inv = nm.inv(h[i][j]); break; } if (col[j] == -1) { add *= fr; continue; } REP(i, t) { if (i == col[j] || h[i][j] == 0) continue; unsigned long long mul = nm.product(inv, h[i][j]); REP(jj, n) { h[i][jj] ^= nm.product(mul, h[col[j]][jj]); } } } ans += add; ll bn = 1LL << n; FOR(b, 1, bn) { ll gb = b ^ (b >> 1); ll bb = (b - 1) ^ ((b - 1) >> 1); // ll bj = count_zero(gb ^ bb); ll bj; ll pc = 0; REP(j, n) { if (((gb ^ bb) >> j) == 1) { bj = j; } pc += EXISTBIT(gb, j); } if (EXISTBIT(gb, bj)) { if (col[bj] != -1) { ll ej = raw[col[bj]]; ll ei = col[bj]; raw[col[bj]] = -1; col[bj] = -1; unsigned long long inv = 0; REP(j, n) { if (EXISTBIT(gb, j) || col[j] != -1 || h[ei][j] == 0) continue; col[j] = ei; raw[ei] = j; inv = nm.inv(h[ei][j]); break; } if (raw[ei] != -1) { add *= frinv; REP(i, t) { if (i == col[raw[ei]] || h[i][raw[ei]] == 0) continue; unsigned long long mul = nm.product(inv, h[i][raw[ei]]); REP(jj, n) { h[i][jj] ^= nm.product(mul, h[ei][jj]); } } } } else { add *= frinv; } } else { unsigned long long inv = 0; REP(i, t) { if (raw[i] != -1 || h[i][bj] == 0) continue; col[bj] = i; raw[i] = bj; inv = nm.inv(h[i][bj]); break; } if (col[bj] == -1) { add *= fr; } else { REP(i, t) { if (i == col[bj] || h[i][bj] == 0) continue; unsigned long long mul = nm.product(inv, h[i][bj]); REP(jj, n) { h[i][jj] ^= nm.product(mul, h[col[bj]][jj]); } } } } ans += __popcount(gb) % 2 ? -add : add; } cout << ans.val(); } int main() { ll t = 1; //cin >> t; while (t--) { solve(); } return 0; }