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

data = [0]*(K+1)
for x in range(K,0,-1):
    p = pow(K//x,N,mod)
    for k in range(2,K//x+1):
        p -= data[k*x]
        p %= mod
    data[x] = p
    ans += x*p
    ans %= mod

###
#print(data)
###
    
print(ans)