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
mod=pow(10,9)+7
n,k=map(int,input().split())
a=[0 for i in range(100000+1)]
ans=0
for i in range(k,0,-1):
    a[i]=k//i
    a[i]=pow(a[i],n,mod)
    j=2*i
    while j<=k:
        a[i]=(a[i]-a[j]+mod)%mod
        j += i
    ans=(ans+a[i]*i)%mod
print(ans)