#include #include #include #define MOD 1000000007 typedef unsigned long long llu; typedef signed long long lld; llu n, m; void powmtr(/* const */ llu* mtr[], llu n, int size, llu* resultVar[]){ int i, j; llu prevmtr[2][size]; llu resultdata[2][size]; for (i = 0; i < 2; i++) { for (j = 0; j < size; j++) { resultdata[i][j] = (i == j ? 1 : 0); prevmtr[i][j] = mtr[i][j]; } } while (n) { if (n & 1) { const llu rd00 = resultdata[0][0]; const llu rd01 = resultdata[0][1]; const llu rd10 = resultdata[1][0]; const llu rd11 = resultdata[1][1]; // puts("resultdata update!"); for (i = 0; i < size; i++) { if (i != size - 1) { resultdata[0][i] = resultdata[1][i] = 0; } resultdata[0][i] += (rd00 * prevmtr[0][i] + rd01 * prevmtr[1][i]) % MOD; resultdata[0][i] %= MOD; resultdata[1][i] += (rd10 * prevmtr[0][i] + rd11 * prevmtr[1][i]) % MOD; resultdata[1][i] %= MOD; // printf("%llu %llu\n", resultdata[0][i], resultdata[1][i]); } } // putchar('\n'); n = (n >> 1); // puts("prevmtr update!"); { const llu pm00 = prevmtr[0][0]; const llu pm01 = prevmtr[0][1]; const llu pm10 = prevmtr[1][0]; const llu pm11 = prevmtr[1][1]; for (i = 0; i < size; i++) { const llu pm0i = prevmtr[0][i]; const llu pm1i = prevmtr[1][i]; if (i != size - 1) { prevmtr[0][i] = prevmtr[1][i] = 0; } prevmtr[0][i] += (pm00 * pm0i + pm01 * pm1i) % MOD; prevmtr[0][i] %= MOD; prevmtr[1][i] += (pm10 * pm0i + pm11 * pm1i) % MOD; prevmtr[1][i] %= MOD; // printf("%llu %llu\n", prevmtr[0][i], prevmtr[1][i]); } } // putchar('\n'); // puts("========================="); } for (i = 0; i < 2; i++) { for (j = 0; j < size; j++) { resultVar[i][j] = resultdata[i][j]; } } } llu solve(llu m){ int i; llu leftMatrix[m + 1]; llu rightMatrixPeace[2][m + 1]; llu* argRightm[2] = {rightMatrixPeace[0], rightMatrixPeace[1]}; llu answer; llu fibPrev = 0, fibNext = 1; for (i = m - 1; i >= 0; i--) { leftMatrix[i] = rightMatrixPeace[1][i] = fibNext; fibPrev += fibNext; fibPrev %= MOD; fibPrev ^= fibNext; fibNext ^= fibPrev; fibPrev ^= fibNext; } for (i = 0; i < m; i++) { rightMatrixPeace[0][i + 1] = rightMatrixPeace[1][i]; } leftMatrix[m] = 0; rightMatrixPeace[0][0] = (rightMatrixPeace[0][1] + rightMatrixPeace[1][1]) % MOD; rightMatrixPeace[1][m] = 0; powmtr(argRightm, n, m + 1, argRightm); // for (i = 0; i < m + 1; i++) printf("%d %llu\n", i, leftMatrix[i]); // for (i = 0; i < 2; i++) { // for (int j = 0; j <= m; j++) { // printf("%d:%d %llu\n", i, j, rightMatrixPeace[i][j]); // } // } answer = (leftMatrix[0] * rightMatrixPeace[0][m] + leftMatrix[1] * rightMatrixPeace[1][m]) % MOD; return answer; } int main(void){ llu answer; scanf("%llu %llu", &n, &m); printf("%llu\n", solve(m)); return 0; }