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=pow(10,9)+7
ans=[0]*(k+1)
# gcdがkiとなる数列。すべてがkiの倍数でかつ少なくとも一つkiを含む
for ki in range(k,0,-1):
    a=k//ki
    ans[ki]=pow(a,n,mod)
    i=2
    while i*ki<=k:
        ans[ki]-=ans[i*ki]
        i+=1
b=0
for ki in range(1,k+1):
    b+=(ans[ki]*ki)%mod
    b%=mod
print(b)
