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
from math import gcd
N,K = map(int,input().split())
MOD = 10**9+7

dp = [1] * (K+1)
for n in range(K//2,0,-1):
    p = pow(K//n,N,MOD)
    for m in range(2*n,K+1,n):
        p -= dp[m]
    dp[n] = p%MOD

ans = 0
for i,n in enumerate(dp):
    ans += i*n
    ans %= MOD
print(ans)