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

gcd = {}
s = 0

for x in range(K,0,-1):
  
    i = K // x
    tmp = pow(i,N,mod)  # 組み合わせ数
    
    if i > 1:
        for j in range(2,i+1):
            tmp -= gcd[j * x]
    
    gcd[x] = tmp
    s += (tmp * x) % mod
    s %= mod

print(s)