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 <cstring>
#include <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <set>
#include <queue>
#include <map>
using namespace std;
typedef long long ll;
#define rep(i,j,k) for(ll i = j; i < k; ++i)
#define per(i,j,k) for(ll i = j; i > k; --i)
int a[10005];
int main() {
        int n; cin >> n;
        ll ans = 0; bool ok = false;
        for(int i = 1; i <= n; ++i) cin >> a[i];
        for(int i = 1; i <= n; ++i) {
                int x; cin >> x;
                if(x != a[i]) ok = true;
                ans += a[i] - x;
        }
        if((n == 1 && ans <= 0) || !ok) return 0 * printf("Yes\n");
        if(ans < 0 && -ans & 1) printf("Yes\n");
        else printf("No\n");
        return 0;
}