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=list(map(int,input().split()))
l=[0]*(K+1)
ans=0
mod=10**9+7

for x in range(K,0,-1):
    l[x]=pow((K//x),N,mod)
    for y in range(2*x,K+1,x):
        l[x]-=l[y]
        l[x]=pow(l[x],1,mod)
    ans+=l[x]*x
    ans=pow(ans,1,mod)
print(ans)