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 = [pow(k // max(i, 1), n, mod) for i in range(k+1)]

for i in range(k, 0, -1):
    for j in range(2*i, k+1, i):
        cnt[i] -= cnt[j]

s = 0
for i in range(k+1):
    s = (s + i*cnt[i]) % mod

print(s)