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

cnt = [0] * (K + 1)

def calc(x):
    M = K // x
    c = pow(M, N, MOD)
    for i in range(x + x, K + 1, x):
        c -= cnt[i]
    cnt[x] = c
    return c * x

ans = 0
for x in range(1, K + 1)[::-1]:
    ans = (ans + calc(x)) % MOD
print(ans)
