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
import sys
input = sys.stdin.readline

mod = 10**9+7

N, K = map(int, input().split())

ans = 0
dp = [None]*(K+1)
for n in reversed(range(1, K+1)):
    L = K//n
    p = pow(L, N, mod)
    for i in range(2, L+1):
        p = (p - dp[n*i]) % mod
    
    dp[n] = p
    ans = (ans + p*n) % mod

print(ans)