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 C# (Mono-mcs 6.8.0.105) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;

namespace contest_Csharp
{
    class Program
    {
        static void Main(string[] args)
        {
            int K = int.Parse(Console.ReadLine());

            //var prop = Console.ReadLine().Split(' ')
            //  .Select(x => int.Parse(x)).ToList();
            //long u = gcd(18, 18);
            long sum = 0;
            int flg = 0;
            for (int i = 0; i < K; i++)
            {
                for (int m = 0; m < K; m++)
                {
                    for (int n = 0; n < K; n++)
                    {
                        
                        long h=gcd(i+1,gcd(n+1,m+1));
                        if (h % 2==0 )
                        {
                            flg++;
                        }
                        sum += h;
                    }
                }
            }
            Console.WriteLine(sum);


        }
        static long gcd(long a, long b)
        {
            long A = Math.Max(a, b);
            long B = Math.Min(a, b);
            long D ;
            while (true)
            {
                D = B;
                B = A % B;
                A = D;
                if (B == 0)
                    break;
            }
            return D;
        }
    }
}