Problem:
Score : 500 points

Problem Statement

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).

Sample Input 1

3 2

Sample Output 1

9

\gcd(1,1,1)+\gcd(1,1,2)+\gcd(1,2,1)+\gcd(1,2,2)
+\gcd(2,1,1)+\gcd(2,1,2)+\gcd(2,2,1)+\gcd(2,2,2)
=1+1+1+1+1+1+1+2=9

Thus, the answer is 9.

Sample Input 2

3 200

Sample Output 2

10813692

Sample Input 3

100000 100000

Sample Output 3

742202979

Be sure to print the sum modulo (10^9+7).

Solution in Pascal (FPC 3.0.4) (judge verdict: Accepted)

const M=1000000007;
function power(a,b:int64):int64;
var t:int64;
begin
if b=0 then power:=1 else begin
t:=power(a*a mod M,b div 2);
if b mod 2=1 then t:=t*a mod M;
power:=t;
end;
end;
var
N,K,i,j:Longint;
now,ans:int64;
memo:Array[1..100000]of Longint;
begin
read(N,K);
for i:=K downto 1 do begin
now:=power(K div i,N);
j:=i+i;
while j<=K do begin
dec(now,memo[j]);
inc(j,i);
end;
memo[i]:=(now mod M+M)mod M;
inc(ans,now*i mod M);
end;
writeln(ans mod M);
end.