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())

ans=0
MOD=10**9+7

cnt=[0]*(K+1)
for x in reversed(range(1,K+1)):
    t = K//x
    cnt_tmp = pow(t,N,MOD)
    t=1
    while (t+1)*x<=K:
        t+=1
        cnt_tmp -= cnt[x*t]
    g = x*cnt_tmp %MOD
    cnt[x]+=cnt_tmp
    ans +=g
    ans%=MOD
print(ans)
