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
# E - Sum of gcd of Tuples (Hard)

n, k = map(int, input().split())
X = [0]*(k+1)
mod = 10**9+7

for x in range(k, 0, -1):
    #X[x] = ((k//x)**n)%mod
    X[x] = pow(k//x, n, mod)
    for x_multi in range(x*2, k+1, x):
        X[x] -= X[x_multi]

print(sum((i*x)for i, x in enumerate(X))%mod)