#include #include #include using namespace std; typedef long long LL; const int maxn = 10000; const LL Six = 166666668; /// 6,2关于mod的乘法逆元 const LL Two = 500000004; const LL mod = 1e9 + 7; /// 尽量这样定义mod ,减少非必要的麻烦 bool book[maxn]; int pri[1300], cnt; /// 素数表 int factor[130]; /// 因子表 void Prime() { memset(book, 0, sizeof(book)); cnt = 0; book[0] = book[1] = 1; for (int i = 2; i < maxn; i++) { if (!book[i]) pri[cnt++] = i; for (int j = 0; j < cnt && pri[j] * i < maxn; j++) { book[i * pri[j]] = 1; if (i % pri[j] == 0) break; } } } inline LL Mod(LL a, LL b) { return (a % mod) * (b % mod) % mod; } inline LL F(LL k, LL n) { /// 求(k*n)^2+k*n return (Mod(k, k) * Mod(Mod(n, n + 1), Mod(n + n + 1, Six)) % mod + Mod(Mod(1 + n, n), Mod(k, Two))) % mod; } int main() { LL n, m; Prime(); while (~scanf("%lld%lld", &n, &m)) { int fac_cnt = 0; /// 素数因子的个数 for (int i = 0; i < cnt; i++) { if (pri[i] > m) break; if (m % pri[i] == 0) { factor[fac_cnt++] = pri[i]; while (m % pri[i] == 0) m /= pri[i]; } } if (m > 1) factor[fac_cnt++] = m; LL sum = F(1LL, n), ans = 0; /// 计算总和sum LL item = 1 << fac_cnt; /// 开始容斥 /// 例如有3个因子,那么item=1<<3=8(1000二进制) /// 然后i从1开始枚举直到7(111二进制),i中二进制的位置1表式取这个位置的因子 /// 例如i=3(11二进制) 表示去前两个因子,i=5(101)表示取第1个和第3个的因子 for (int i = 1; i < item; i++) { int num = 0, x = 1; for (int j = 0; j < fac_cnt; j++) { if (1 & (i >> j)) num++, x *= factor[j]; } if (num & 1) ans = (ans + F(x, n / x)) % mod; /// 根据容斥,取奇数个因子时,应加上 else ans = ((ans - F(x, n / x)) % mod + mod) % mod; } printf("%lld\n", ((sum - ans) % mod + mod) % mod); } return 0; }