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
mod = 10 ** 9 + 7

n, k = list(map(int, input().split()))
c = {i: pow(k//i, n, mod) for i in range(1, k+1)}
for i in range(k, 0, -1):
    for j in range(2*i, k+1, i):
        c[i] -= c[j]
_sum = 0
for x in range(1, k+1):
    _sum += c[x] * x % mod
print(_sum % mod)
