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 <bits/stdc++.h>
#define x first
#define y second
#define gcd(x, y) __gcd((x), (y))
using namespace std;

using i64 = long long;
using f64 = double;
using pii = pair<int, int>;

const int N = 1e5 + 5;

i64 a[N], b[N], c[N];

int n;
i64 sp, sn, t;

int main() {
#ifdef HOME
	freopen("atc.in", "r", stdin);
	freopen("atc.out", "w", stdout);
#endif
	ios::sync_with_stdio(false);
	cin.tie(0), cout.tie(0);
	
	cin >> n;	
	for (int i = 0; i < n; ++i)
		cin >> a[i];
	for (int i = 0; i < n; ++i)
		cin >> b[i];

	for (int i = 0; i < n; ++i) {
		c[i] = a[i] - b[i];
		if (c[i] > 0)
			sp+= c[i];
		else
			sn-= c[i];  }

	if (sn - 2 * sp >= 0)
		cout << "Yes\n";
	else
		cout << "No\n";

	return 0; }