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=[int(x) for x in input().split()]
ans=0
l=[0]*(k+1)
i=k
mod=1000000007
while i>0:
    l[i]=pow(k//i,n,mod)
    j=2*i
    while j<=k:
        l[i]=(l[i]-l[j]+mod)%mod
        j+=i
    i-=1
for i in range(1,k+1):
    ans+=(l[i]*i)%mod
print(ans%mod)
