Codeforces Round #280 (Div. 2) D. Vanya and Computer Game 数学

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原文链接：http://www.cnblogs.com/jhz033/p/5917613.html

探讨Vanya与Vova如何在游戏中高效合作消灭怪物。利用循环节原理优化算法，通过离线处理和余数计算确定最后一击的执行者。

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Vanya and his friend Vova play a computer game where they need to destroy n monsters to pass a level. Vanya's character performs attack with frequency x hits per second and Vova's character performs attack with frequency y hits per second. Each character spends fixed time to raise a weapon and then he hits (the time to raise the weapon is 1 / x seconds for the first character and 1 / y seconds for the second one). The i-th monster dies after he receives ai hits.

Vanya and Vova wonder who makes the last hit on each monster. If Vanya and Vova make the last hit at the same time, we assume that both of them have made the last hit.

Input

The first line contains three integers n,x,y (1 ≤ n ≤ 105, 1 ≤ x, y ≤ 106) — the number of monsters, the frequency of Vanya's and Vova's attack, correspondingly.

Next n lines contain integers ai (1 ≤ ai ≤ 109) — the number of hits needed do destroy the i-th monster.

Output

Print n lines. In the i-th line print word "Vanya", if the last hit on the i-th monster was performed by Vanya, "Vova", if Vova performed the last hit, or "Both", if both boys performed it at the same time.

Examples

input

output

Vanya
Vova
Vanya
Both

input

2 1 1
1
2

output

Both
Both

Note

In the first sample Vanya makes the first hit at time 1 / 3, Vova makes the second hit at time 1 / 2, Vanya makes the third hit at time 2 / 3, and both boys make the fourth and fifth hit simultaneously at the time 1.

In the second sample Vanya and Vova make the first and second hit simultaneously at time 1.

题意：va每秒可以打x次，vo每秒可以打y次，求第a[i]次是谁打的；

思路：循环节为x/gcd(x,y)+y/gcd(y,z);

　　　离线处理，最多2e6次左右，余数暴力；

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define pi (4*atan(1.0))
#define eps 1e-14
const int N=2e5+10,M=4e6+10,inf=1e9+10,mod=1e9+7;
int ans[N];
struct is
{
    int a;
    int pos;
    bool operator <(const is &b)const
    {
        return a<b.a;
    }
}a[N];
int gcd(int x,int y)
{
    return y==0?x:gcd(y,x%y);
}
int main()
{
    int n,x,y;
    scanf("%d%d%d",&n,&x,&y);
    int len=x/gcd(x,y)+y/gcd(x,y);
    for(int i=1;i<=n;i++)
    scanf("%d",&a[i].a),a[i].a%=len,a[i].pos=i;
    sort(a+1,a+n+1);
    int va=0;
    int vo=0;
    double xx=1.0/x;
    double yy=1.0/y;
    for(int i=1;i<=n;i++)
    {
        while(va+vo<a[i].a)
        {
            if(va*xx+xx<vo*yy+yy)
            va++;
            else
            vo++;
        }
        ans[a[i].pos]=(va*xx-vo*yy>eps?1:-1);
        if(a[i].a==len-1||a[i].a==0)ans[a[i].pos]=0;
    }
    for(int i=1;i<=n;i++)
    if(ans[i]==1)
        printf("Vanya\n");
    else if(ans[i]==0)
        printf("Both\n");
    else
        printf("Vova\n");
    return 0;
}