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
import math
N,K= map(int, input().split())
a=[0]*(K+1)
co=0
mod=(10**9+7)
for i in range(K,0,-1):

    b=K//i
    t=2*i
    m=0
    while t<=K:
        m=m+a[t]
        t+=i
    c=pow(b,N,mod)
    a[i]=c-m
    co+=(a[i]*i)%mod


print(co%mod)
