/* -*- coding: utf-8 -*- * * 510.cc: No.510 二次漸化式 - yukicoder */ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; /* constant */ const int MAX_N = 100000; const int MAX_E2 = 1 << 18; // 262144 const int N = 4; typedef long long ll; const ll MOD = 1000000007; /* typedef */ typedef vector vi; typedef queue qi; typedef pair pii; struct Vec { ll v[N]; Vec(): v() {} Vec(const ll _v[N]) { memcpy(v, _v, sizeof(v)); } }; const ll IDV0[] = {1, 1, 1, 1}; const Vec V0(IDV0); struct Mat { ll m[N][N]; Mat() {} Mat(const ll _m[N][N]) { memcpy(m, _m, sizeof(m)); } void init(const ll _m[N][N]) { memcpy(m, _m, sizeof(m)); } Mat operator*(const Mat &a) const { Mat r; for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) { r.m[i][j] = 0; for (int k = 0; k < N; k++) r.m[i][j] += m[i][k] * a.m[k][j] % MOD; r.m[i][j] %= MOD; } return r; } Vec operator*(const Vec &v) const { Vec r; for (int i = 0; i < N; i++) { r.v[i] = 0; for (int j = 0; j < N; j++) r.v[i] += m[i][j] * v.v[j] % MOD; r.v[i] %= MOD; } return r; } void print() { for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) printf("%lld ", m[i][j]); putchar('\n'); } } }; const ll ID[N][N] = { {1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, 0, 1}, {0, 0, 0, 1} }; Mat IDMAT(ID); struct SegTreeMat { int n, e2; Mat nodes[MAX_E2]; SegTreeMat() {} void init(int _n) { n = _n; for (e2 = 1; e2 < n; e2 <<= 1); fill(nodes, nodes + MAX_E2, IDMAT); } Mat get(int i) { return nodes[e2 - 1 + i]; } void setx(int i, ll x) { int j = e2 - 1 + i; nodes[j].m[0][2] = x; j = (j - 1) / 2; for (;;) { nodes[j] = nodes[j * 2 + 2] * nodes[j * 2 + 1]; if (j == 0) break; j = (j - 1) / 2; } } void sety(int i, ll y) { int j = e2 - 1 + i; nodes[j].m[1][1] = y; nodes[j].m[2][1] = 2 * y % MOD; nodes[j].m[2][2] = y * y % MOD; j = (j - 1) / 2; for (;;) { nodes[j] = nodes[j * 2 + 2] * nodes[j * 2 + 1]; if (j == 0) break; j = (j - 1) / 2; } } Mat mul_range(int r0, int r1, int k, int i0, int i1) { if (r1 <= i0 || i1 <= r0) return IDMAT; if (r0 <= i0 && i1 <= r1) return nodes[k]; int im = (i0 + i1) / 2; Mat v0 = mul_range(r0, r1, k * 2 + 1, i0, im); Mat v1 = mul_range(r0, r1, k * 2 + 2, im, i1); return v1 * v0; } Mat mul_range(int r0, int r1) { return mul_range(r0, r1, 0, 0, e2); } }; /* global variables */ SegTreeMat st; /* subroutines */ /* main */ // a{i+1} |1 0 xi 0| ai // b{i+1} = |0 yi 0 1| bi // b{i+1}^2 |0 2yi yi^2 1| bi^2 // 1 |0 0 0 1| 1 int main() { int n, qn; scanf("%d%d", &n, &qn); //printf("n=%d, qn=%d\n", n, qn); st.init(n); while (qn--) { while (getchar() != '\n'); char op; int i; scanf("%c %d", &op, &i); if (op == 'x' || op == 'y') { int v; scanf("%d", &v); //printf("%c %d %d\n", op, i, v); if (op == 'x') st.setx(i, v); else st.sety(i, v); } else { //printf("%c %d\n", op, i); Mat mi = st.mul_range(0, i); //printf("mi=\n"), mi.print(); Vec vv = mi * V0; printf("%lld\n", vv.v[0]); } } //for (int i = 0; i < n; i++) printf("%d:\n", i), st.get(i).print(); return 0; }