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())
x=[0]*(k+1)
y=0

# 最大公約数がその数になる組合せで場合わけ、後ろから埋めて重複を引く
for i in range(k,0,-1):
    m=k//i
    x[i]=pow(k//i,n,mod)
    for j in range(1,m):
        x[i]-=x[i*(j+1)]
        x[i]%=mod

ans=0
for i in range(1,k+1):
    ans+=x[i]*i
    ans%=mod

print(ans)