#include using namespace std; using T = long long; using vvt = vector>; constexpr long long MOD = 1'000'000'007; long long umod(long long x, const long long mod = MOD) {return ((x % mod) + mod) % mod;} // unsigned mod. always returns a non-negative value long long inv(long long x, const long long mod = MOD) { // Finds a multiplicative inverse of x modulo mod by Extended Euclidean Algorithm long long a = umod(x); long long b = mod; long long c = 1LL; long long d = 0LL; long long q; long long r; while (b != 1){ q = a / b; r = a % b; a = b; b = r; long long tmp = c; c = d; d = tmp - q * d; } return umod(d); } auto identity_mat(int n){ vvt I(n, vector(n, 0)); for (int i = 0; i != n; ++i) I[i][i] = 1; return I; } auto matmul(vvt a, vvt b, const long long mod = MOD){ int n_row = a.size(); int n_col = b[0].size(); assert(a[0].size() == b.size()); vvt c(n_row, vector(n_col, 0)); for (int i = 0; i != n_row; ++i){ for (int j = 0; j != n_col; ++j){ for (int k = 0; k != b.size(); ++k){ c[i][j] = (c[i][j] + a[i][k] * b[k][j]) % mod; } } } return c; } auto matpow(vector> mat, long long n, const long long mod = MOD){ // a^n を求める。 assert(mat.size() == mat[0].size()); auto ans = identity_mat(mat.size()); while (n){ if (n & 1) ans = matmul(ans, mat, mod); mat = matmul(mat, mat, mod); n >>= 1; } return ans; } auto invmat(const vector> &mat, const long long mod = MOD){ vvt ans = {{0LL, 0LL}, {0LL, 0LL}}; long long a = mat[0][0]; long long b = mat[0][1]; long long c = mat[1][0]; long long d = mat[1][1]; if (d != 0LL){ ans[0][0] = inv(a - ((b * c) % mod) * inv(d) % mod); }else{ ans[0][0] = 0LL; } ans[1][0] = inv(b - ((a * d) % mod) * inv(c) % mod); ans[0][1] = inv(c - ((d * a) % mod) * inv(b) % mod); ans[1][1] = inv(d - ((c * b) % mod) * inv(a) % mod); return ans; } auto matminus(vector> a, vector> b){ int n_row = a.size(); int n_col = a[0].size(); assert(b.size() == n_row); assert(b[0].size() == n_col); vvt c(n_row, vector(n_col, 0)); for (int i = 0; i != n_row; ++i){ for (int j = 0; j != n_col; ++j){ c[i][j] = umod(a[i][j] - b[i][j]); } } return c; } int main() { long long N; int M; cin >> N >> M; vvt mat = {{1LL, 1LL},{1LL, 0LL}}; auto Fm = matpow(mat, M); auto Fmn1 = matpow(Fm, N + 1LL); auto Fm_minus_I = matminus(Fm, identity_mat(2)); auto Finv = invmat(Fm_minus_I); auto Fcum = matmul(Finv, matminus(Fmn1, Fm)); cout << Fcum[1][0] << endl; return 0; }