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
N,K = map(int,input().split())
mod = 10**9+7
ans = 0
X_gcd = [0]*(K+1)
for X in reversed(range(1,K+1)):
    X_gcd[X] = pow(K//X,N,mod)
    
    for nX in range(2*X,K+1,X):
        X_gcd[X] -= X_gcd[nX]
        
    ans = (ans+(X%mod)*(X_gcd[X]%mod))%mod
print(ans%mod)