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 <iostream>
#include <vector>
#include <string>
#include <math.h>
#include <algorithm>
#include <queue>
#define INF 9999999999
using namespace std;
typedef long long int ll;

int main() {
	int N;
	cin >> N;
	ll A = 0, B = 0;
	vector<ll> a(N), b(N), AB(N), BA(N);
	for (int i = 0; i < N; i++) {
		cin >> a[i];
		A += a[i];
	}
	for (int i = 0; i < N; i++) {
		cin >> b[i];
		B += b[i];
	}

	ll af = 0, bf = 0;
	for (int i = 0; i < N; i++) {
		AB[i] = a[i] - b[i];
		BA[i] = b[i] - a[i];
		if (AB[i] > 0) bf -= AB[i];
		if (BA[i] > 0) af -= BA[i];
	}

	af += (B - A) * 2;
	bf += (B - A);

	if (af == bf && af >= 0 && bf >= 0 && af % 2 == 0) cout << "Yes" << endl;
	else cout << "No" << endl;
	return 0;
}