Problem:
Score : 300 points

Problem Statement

You are given two integer sequences of length N: a_1,a_2,..,a_N and b_1,b_2,..,b_N.
Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal.

Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:

Add 2 to a_i.

Add 1 to b_j.

Constraints

1 ≤ N ≤ 10 000

0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 .. a_N
b_1 b_2 .. b_N

Output

If we can repeat the operation zero or more times so that the sequences a and b become equal, print Yes; otherwise, print No.

Sample Input 1

3
1 2 3
5 2 2

Sample Output 1

Yes

For example, we can perform three operations as follows to do our job:

First operation: i=1 and j=2. Now we have a = \{3,2,3\}, b = \{5,3,2\}.

Second operation: i=1 and j=2. Now we have a = \{5,2,3\}, b = \{5,4,2\}.

Third operation: i=2 and j=3. Now we have a = \{5,4,3\}, b = \{5,4,3\}.

Sample Input 2

5
3 1 4 1 5
2 7 1 8 2

Sample Output 2

No

Sample Input 3

5
2 7 1 8 2
3 1 4 1 5

Sample Output 3

No

Solution in C# (.NET Core 3.1.201) (judge verdict: Accepted)

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

namespace ConsoleApp2
{
    class Program
    {
        static int N;
        static long mod = 1000000007;
        static char[] az = Enumerable.Range('a', 'z' - 'a' + 1).Select(i => (Char)i).ToArray();
        static void Main(string[] args)
        {
            var N = long.Parse(Console.ReadLine());
            var A = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            var B = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            //var N = long.Parse(Console.ReadLine());
            //var A = new int[N];
            var C = new long[N];
            long sum = 0L;
            for (int i = 0; i < N; i++)
            {
                C[i] = A[i] - B[i];

                if(C[i] < 0)
                {
                    var tmp = Abs(C[i]);
                    sum += (tmp+1) / 2;
                    C[i] = ((tmp % 2 == 0) ? 0 : 1);
                }
            }

            if(sum >= C.Sum())
            {
                Console.WriteLine("Yes");
            }
            else
            {
                Console.WriteLine("No");
            }

            
            //R = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            //var S = Console.ReadLine();

        }
        // ユークリッドの互除法 
        public static int Gcd(int a, int b)
        {
            if (a < b)
                // 引数を入替えて自分を呼び出す
                return Gcd(b, a);
            while (b != 0)
            {
                var remainder = a % b;
                a = b;
                b = remainder;
            }
            return a;
        }
    }
}