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#include <bitset> | |
#include <iostream> | |
#include <vector> | |
#include <ext/pb_ds/assoc_container.hpp> | |
using namespace std; | |
using namespace __gnu_pbds; | |
#define MAXN 1000001 | |
#define MOD 1000000007 | |
template <size_t N> void | |
sieve(int mobius[]) { | |
bitset<N> is_comp; | |
vector<int> prime; | |
mobius[1] = 1; | |
for (int p = 2; p != N; ++p) { | |
if (!is_comp.test(p)) { | |
prime.push_back(p); | |
mobius[p] = -1; | |
} | |
for (vector<int>::iterator i = prime.begin(); i != prime.end(); ++i) { | |
const int q = *i; | |
if (p * q >= N) break; | |
is_comp.set(p * q); | |
if (p % q == 0) { | |
mobius[p * q] = 0; | |
break; | |
} else mobius[p * q] = -mobius[p]; | |
} | |
} | |
} | |
int N, K, L, H; | |
int mobius[MAXN]; | |
long long psum(int n) { | |
static cc_hash_table<int, long long> mem; | |
if (n < MAXN) return mobius[n]; | |
cc_hash_table<int, long long>::point_iterator it; | |
it = mem.find(n); | |
if (it != mem.end()) | |
return it->second; | |
long long r = 1; | |
for (int i = 2, j; i <= n; i = j + 1) { | |
j = n / (n / i); | |
r -= psum(n / i) * (j - i + 1) % MOD; | |
if (r < 0) r += MOD; | |
} | |
return mem[n] = r; | |
} | |
long long modpow(long long b, int e) { | |
long long r = 1; | |
do { | |
if (e & 1) r = r * b % MOD; | |
if (e > 1) b = b * b % MOD; | |
} while (e >>= 1); | |
return r; | |
} | |
int main() { | |
sieve<MAXN>(mobius); | |
for (int i = 0; i != MAXN; ++i) { | |
mobius[i] = mobius[i] + mobius[i - 1]; | |
if (mobius[i] >= MOD) mobius[i] -= MOD; | |
if (mobius[i] < 0) mobius[i] += MOD; | |
} | |
cin >> N >> K >> L >> H; | |
H = H / K; L = (L - 1) / K; | |
long long r = 0; | |
for (int i = 1, j; i <= H; i = j + 1) { | |
if (L / i == 0) j = H / (H / i); | |
else j = min(H / (H / i), L / (L / i)); | |
r += modpow(H / i - L / i, N) * (psum(j) - psum(i - 1)) % MOD; | |
if (r >= MOD) r -= MOD; | |
if (r < 0) r += MOD; | |
} | |
cout << r << '\n'; | |
} |