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>
using namespace std;

int n;
vector<long long> a, b;
template <class T>
void readVector(int n, vector<T> &v){
	for(int i=0; i<n; ++i){
		T t;
		cin >> t;
		v.push_back(t);
	}
}

int main(){
//	cin.tie(0);
//	ios::sync_with_stdio(false);
	cin >> n;
	readVector(n, a);
	readVector(n, b);
	for(int i=0; i<n-1; ++i){
		long long mi = min(a[i], b[i]);
		a[i] -= mi;
		b[i] -= mi;
		long long t = max(0ll, (b[i] - a[i] + 1) / 2);
		a[i] += 2 * t;
		b[i+1] += t;
		t = max(0ll, a[i] - b[i]);
		b[i] += t;
		a[i+1] += 2*t;
	}
	cout << (a[n-1] <= b[n-1] ? "Yes" : "No") << "\n";
}