Problem:
Score : 200 points

Problem Statement

There are some animals in a garden. Each of them is a crane with two legs or a turtle with four legs.

Takahashi says: "there are X animals in total in the garden, and they have Y legs in total." Determine whether there is a combination of numbers of cranes and turtles in which this statement is correct.

Constraints

1 \leq X \leq 100

1 \leq Y \leq 100

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X Y

Output

If there is a combination of numbers of cranes and turtles in which the statement is correct, print Yes; otherwise, print No.

Sample Input 1

3 8

Sample Output 1

Yes

The statement "there are 3 animals in total in the garden, and they have 8 legs in total" is correct if there are two cranes and one turtle. Thus, there is a combination of numbers of cranes and turtles in which the statement is correct.

Sample Input 2

2 100

Sample Output 2

No

There is no combination of numbers of cranes and turtles in which this statement is correct.

Sample Input 3

1 2

Sample Output 3

Yes

We also consider the case in which there are only cranes or only turtles.

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define f(i, k, n) for (int i = k; k < n ? i < n : i > n; k < n ? i += 1 : i -= 1)
#define ll long long
#define pb push_back
#define fr first
#define sc second
#define len(s) s.size()
#define all(v) v.begin(), v.end()
#define tr(it, v) for (auto &it : v)
#define bit(x) __builtin_popcount(x)
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef map<int, int> mii;
typedef vector<pii> vpii;
typedef vector<vi> vvi;
    // =================
void impgraph(int n, int m);
void dfs(int u,int par);

const int mod = 1e7;
const int N = 3e5 + 1;

vi g[N];
int a[N];

void solve()
{
    int n, m, ans = 0, k=0;
    cin>>n>>m;
    f(i,0,n) {
        ans=0;
        ans+=i*2+(n-i)*4;
        if(ans==m) {
            cout<<"YES";
            return;
        }
    }
    cout<<"NO";
}

int main()
{
#ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
#endif
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);

    int t = 1;
    //cin >> t;
    while (t--)
        solve();
    return 0;
}

void impgraph(int n, int m)
{
    int i, u, v;
    while (m--)
    {
        cin >> u >> v;
        g[u].pb(v);
        g[v].pb(u);
    }
}

void dfs(int u,int par)
{
    a[u] = 1;
    for (int v : g[u])
    {
        if (a[v])
            continue;
        dfs(v,0);
    }
}