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 <algorithm>
#include <cmath>
#include <cstring>
#include <cstdio>
#include <map>
#include <stack>
#include <queue>
#include <set>
#include <cstdlib>
#include <stack>
#include <vector>
#define INF 0x3f3f3f3f
#define MOD 1000000009
# define FOR(i,a,n) for(register int i=a; i<=n; ++i)
# define FDR(i,a,n) for(register int i=a; i>=n; --i)
typedef long long ll;
typedef unsigned long long ull;

inline int scan() {
    int x=0,f=1; char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-') f=-1; ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0'; ch=getchar();}
    return x*f;
}
inline void Out(int a) {
    if(a<0) {putchar('-'); a=-a;}
    if(a>=10) Out(a/10);
    putchar(a%10+'0');
}
using namespace std;
const int maxn = 10005;
int a[maxn];
int b[maxn];
int c[maxn];
int main()
{
    int n;
    cin >> n;
    ll sum1 = 0, sum2 = 0;
    for(int i = 1; i <= n; i++)
    {
        cin >> a[i];
        sum1 += a[i];
    }
    for(int i = 1; i <= n; i++)
    {
        cin >> b[i];
        sum2 += b[i];
    }
    ll sum3 = 0;
    for(int i = 1; i <= n; i++)
    {
        if(a[i] > b[i])sum3 += a[i]-b[i];
    }
    bool ok = true;
    if((sum2-sum1) < 0 || sum3 > (sum2-sum1) )ok = false;
    int ji = 0;
    for(int i = 1; i <= n; i++)
    {
        if(b[i] > a[i])
        {
            if((b[i]-a[i])%2 == 1)ji++;
        }
    }
    if(ji%2 == 0 && ji != 0)ok = false;
    if(ok)cout << "Yes" << endl;
    else cout << "No" << endl;
    return 0;
}
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