#include #include using namespace std; using namespace atcoder; //using mint = modint1000000007; using mint = atcoder::modint; const int mod = 1000000007; const int mod2 = mod - 1; //using mint = modint998244353; //const int mod = 998244353; //const int INF = 1e9; //const long long LINF = 1e18; #define rep(i, n) for (int i = 0; i < (n); ++i) #define rep2(i,l,r)for(int i=(l);i<(r);++i) #define rrep(i, n) for (int i = (n-1); i >= 0; --i) #define rrep2(i,l,r)for(int i=(r-1);i>=(l);--i) #define all(x) (x).begin(),(x).end() #define allR(x) (x).rbegin(),(x).rend() #define endl "\n" #define P pair template inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; } template inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; } // 素因数分解 vector> PrimeFactorization(long long n) { vector> ret; for (long long i = 2; i*i <= n; i++) { int c = 0; while (n%i == 0) { // 素数で割り切れなくなるまで割っていく c++;//割った個数を配列に足す n /= i; } if (0 != c) ret.push_back({ i,c }); if (1 == n) break; } if (1 != n) ret.push_back({ n,1 }); return ret; } vector> mul(vector>&A, vector>&B) { vector> C(A.size(), vector(B[0].size())); rep(i, A.size()) rep(j, B[0].size()) rep(k, A[0].size()) C[i][j] += A[i][k] * B[k][j]; //rep(i, A.size()) rep(j, B[0].size()) rep(k, A[0].size()) C[i][j] += A[i][k] & B[k][j]; return C; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); mint::set_mod(mod2); int n; cin >> n; long long k; cin >> k; auto list = PrimeFactorization(n); mapmp; bool chk = false; rep(i, list.size()) { mp[list[i].first] += list[i].second; if (list[i].first > 3)chk = true; } while (chk && (k--)) { chk = false; mapnmp; for (auto[k, v] : mp) { auto list = PrimeFactorization(k + 1); for (auto[p, c] : list) { nmp[p] += v * c; if (p > 3)chk = true; } } swap(mp, nmp); } if (k > 0) { vector> mans(2, vector(2)); rep(i, 2)mans[i][i] = 1; vector> mpow(2, vector(2)); mpow[0][1] = 2; mpow[1][0] = 1; while (k > 0) { if (1 == k % 2) mans = mul(mpow, mans); mpow = mul(mpow, mpow); k /= 2; } mapnmp; nmp[2] = mans[0][0] * mp[2] + mans[0][1] * mp[3]; nmp[3] = mans[1][0] * mp[2] + mans[1][1] * mp[3]; swap(mp, nmp); } mint ans = 1; for (auto[k, v] : mp) ans *= pow_mod(k, v.val(), mod); cout << ans.val() << endl; return 0; }