A. Vladik and Courtesy

At regular competition Vladik and Valera won a andb candies respectively. Vladik offered 1 his candy to Valera. After that Valera gave Vladik 2 his candies, so that no one thought that he was less generous. Vladik for same reason gave3 candies to Valera in next turn.

More formally, the guys take turns giving each other one candy more than they received in the previous turn.

This continued until the moment when one of them couldn’t give the right amount of candy. Candies, which guys got from each other, theydon’t consider as their own. You need to know, who is the first who can’t give the right amount of candy.

Input

Single line of input data contains two space-separated integers a, b (1 ≤ a, b ≤ 10⁹) — number of Vladik and Valera candies respectively.

Output

Pring a single line "Vladik’’ in case, if Vladik first who can’t give right amount of candy, or "Valera’’ otherwise.

Examples

Input

1 1

Output

Valera

Input

7 6

Output

Vladik

Note

Illustration for first test case:

Illustration for second test case:

很水的一道题，给出 a和 b现在由的糖果数量，a先扔出去1个，b扔出去2个，a扔出去3个，依次，问谁到最后手里的糖果不够扔出去的？

//1#if 0#include<bits/stdc++.h>using namespace std;int main(){int a,b;cin>>a>>b;for(int i=1; ; i++){if(i%2==1){a-=i;}else{b-=i;}if(a<0){cout<<"Vladik"<<endl;break;}if(b<0){cout<<"Valera"<<endl;break;}}}#endif