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
l=[0]*(k+1)
 
for i in range(k,0,-1):
    l[i]=pow(k//i,n,mod)
    for j in range(2*i,k+1,i):
        l[i]-=l[j]
        l[i]%=mod
    ans+=l[i]*i
    ans%=mod
 
print(ans)