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<math.h>

using namespace std;

int main(void) {
  int a[10000] = {};
  int b[10000] = {};
  int n;

  long b_max = pow(10, 9);
  //cout << b_max << endl;
  //cout << b_max * 10000 << endl;

  cin >> n;

  int i;

  int sum_a = 0;
  int sum_b = 0;
  long max_sum = 0;

  for(i = 0; i < n; i++) {
    cin >> a[i];
    sum_a += a[i];
  }

  for(i = 0; i < n; i++) {
    cin >> b[i];
    sum_b += b[i];
    if (b[i] == 0) {
      continue;
    }
    if (a[i] == 0) {
      // a[i] == 0 && b[i] != 0のとき、制約条件で絶対に一致することがない。
      cout << "No" << endl;
      return 0;
    }
    max_sum += b_max;
  }

  if (sum_b < sum_a) {
    cout << "No" << endl;
    return 0;
  }

  if (max_sum - sum_b < sum_b - sum_a) {
    cout << "No" << endl;
    return 0;
  } else {
    cout << "Yes" << endl;
    // cout << sum_a << "," << sum_b << endl;
  }

  return 0;
}