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 = 10**9+7

n,k=map(int,input().split())
ans=0

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

print(ans%MOD)