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())
# 1以上k以下の整数がn個
mod=int(1e+9 + 7)
d=[0]*(k+1)
ans=0
for i in range(k,0,-1):
      m=k//i
      d[i]=pow(m,n, mod) 
      d[i]-=sum([d[j*i]for j in range(2,m+1)])
      ans+=(d[i]*i)%mod
print((ans)%mod)
#print(d)

