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
MODINT = 10**9 + 7

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

ans = 0
q = [0] * (K + 1)

for i in range(K, 0, -1):
    q[i] = pow(K//i, N, MODINT)
    for j in range(i*2, K+1, i):
        q[i] -= q[j]
        
    ans += (q[i]*i) % MODINT
    
print(ans % MODINT)