Consider sequences \\{A_1,...,A_N\\} of length N consisting of integers between 1 and K (inclusive).

There are K^N such sequences. Find the sum of \gcd(A_1, ..., A_N) over all of them.

Since this sum can be enormous, print the value modulo (10^9+7).

Here \gcd(A_1, ..., A_N) denotes the greatest common divisor of A_1, ..., A_N.

Constraints

* 2 \leq N \leq 10^5
* 1 \leq K \leq 10^5
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N K


Output

Print the sum of \gcd(A_1, ..., A_N) over all K^N sequences, modulo (10^9+7).

Examples

Input

3 2


Output

9


Input

3 200


Output

10813692


Input

100000 100000


Output

742202979
#include <stdio.h>
#define mod 1000000007
typedef long long ll;

ll mpow(ll a, ll b) {
  ll ans = 1;
  while(b) {
    if(b & 1) ans *= a, ans %= mod;
    a *= a, a %= mod, b >>= 1;
  }
   return ans;
}

int main(void) {
  ll i, j, k, n, ans = 0;
  scanf("%lld%lld", &n, &k);
  ll cnt[k + 1];
  for(i = k; i; --i) {
    cnt[i] = mpow(k / i, n);
    for(j = 2; i * j <= k; ++j) cnt[i] += mod - cnt[i * j], cnt[i] %= mod;
    ans += cnt[i] * i, ans %= mod;
  }
  printf("%lld", ans);
  return 0;
}