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
dp = [0] * (K+5)
ans = 0
for k in range(K, 0, -1):
    dp[k] = pow(K//k, N, MOD)

    i = 2
    while k * i <= K:
        dp[k] -= dp[k*i]
        i += 1
    # print(k, dp)
    ans += k * dp[k]
    ans %= MOD
# print(dp)
print(ans)
