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 <algorithm>
#include <iostream>
#include <map>
#include <numeric>
#include <set>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
#include <queue>
#define MOD (1000000007l)
#define rep(i, n) for(long i = 0; i < (n); i++)

using namespace std;

void solve() {
  long N;
  cin >> N;
  vector<long> A(N), B(N);
  rep (i, N) cin >> A[i];
  rep (i, N) cin >> B[i];

  long marginA = 0;
  long marginB = 0;

  rep (i, N) {
    if (A[i] < B[i]) marginA += B[i] - A[i];
    else marginB += A[i] - B[i];
  }

  if (marginA >= marginB * 2) cout << "Yes" << endl;
  else cout << "No" << endl;
}

int main(void) {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout.precision(12);
  solve();
  return 0;
}