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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

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

namespace AtCoderCs
{

    class Program
    {

        const int Mod = 1000000007;

        static void Main()
        {

            var Arg = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            var N = Arg[0];
            var K = Arg[1];
            var Result = K;
            var IsCalculated = new bool[K];

            for (int i = 1; i < K; i++)
            {

                if (!IsCalculated[i - 1]) 
                {

                    var PaternSum = (pw(K / i, N) * i) % Mod;
                    Result += PaternSum % Mod;
                    IsCalculated[i - 1] = true;

                    for (int j = i + i; j < K; j += i)
                    {

                        var PaternSumJ = (pw(K / j, N) * i) % Mod;
                        Result += PaternSum % Mod;
                        IsCalculated[j - 1] = true;

                    }

                }

            }

            Console.WriteLine(Result);


        }

        static long pw(long Base, long Dim)
        {

            long Result = 1;
            for (var i = 0; i < Dim; i++)
            {

                Result *= Base;
                Result %= Mod;

            }

            return Result;

        }

    }
}