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())
l = [0 for i in range(k + 1)]
ans = 0
mod = 1000000007
for i in range(k, 0, -1):
    l[i] = pow(k // i, n, mod)
    tmp = 2 * i
    while tmp <= k:
        l[i] -= l[tmp]
        tmp += i
for i in range(k + 1):
    ans += i * l[i]
    ans %= mod
print(ans)