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: Wrong Answer)

using System;
using System.Text;
using System.Collections.Generic;
using static System.Math;
using System.Linq;
using static System.Array;

namespace ConsoleApp2
{
    class Program
    {
        static long N;
        static long K;
        static long[] ans;
        static void Main(string[] args)
        {
            var NK = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            N = NK[0];
            K = NK[1];

            ans = new long[K + 1];
            long tmp = 0;
            for (int i = (int)K; i >= 1; i--)
            {
                ans[i] = Cul(i);
                tmp += i * ans[i];
            }
            Console.WriteLine(tmp);
        }

        static long Cul(int num)
        {
            var res = (long)Pow((K/num),N);

            for (long i = 2*num; i <= K; i += num)
            {
                res -= ans[i];
            }
            return res;
        }

    }    
}