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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<cstring>
#include<string>
#include<iostream>
#include<algorithm>
#include<map>
using namespace std;
long long a[10050],b[10050],sum1,sum2;
int main(){
	int n,dis1,dis2;
	scanf("%d",&n);
	sum1=0;
	sum2=0;
	dis1=0;
	dis2=0;
	for(int i=1;i<=n;i++) scanf("%lld",&a[i]);
	for(int j=1;j<=n;j++) scanf("%lld",&b[j]);
	for(int i=1;i<=n;i++){
		if(a[i]<b[i]){
			sum1=sum1+b[i]-a[i];
			dis2++;
			if((b[i]-a[i])%2!=0&&b[i]-a[i]>1){
				dis1+=(b[i]-a[i]-1)/2;
			}
		}
		else if(a[i]>b[i]) sum2=sum2+a[i]-b[i];
	}
	if(sum1<2*sum2) printf("No\n");
	else{
		if(sum1%2==0&&dis2>1&&dis1<sum2) printf("No\n");
		else printf("Yes\n");
	}
}