Pagodas

D - Pagodas

Time Limit:1000MS     Memory Limit:65536KB     64bit IO Format:%I64d & %I64u

Submit Status

Description

n pagodas were standing erect in Hong Jue Si between the Niushou Mountain and the Yuntai Mountain, labelled from 1 to n. However, only two of them (labelled a and b, where 1\le a\neq b\le n) withstood the test of time. 

Two monks, Yuwgna and Iaka, decide to make glories great again. They take turns to build pagodas and Yuwgna takes first. For each turn, one can rebuild a new pagodas labelled i~(i\not\in\{a,b\}~and~1\le i\le n) if there exist two pagodas standing erect, labelled j and krespectively, such that i=j+k or i=j-k. Each pagoda can not be rebuilt twice. 

This is a game for them. The monk who can not rebuild a new pagoda will lose the game.

Input

The first line contains an integer t~(1\le t\le 500) which is the number of test cases. 
For each test case, the first line provides the positive integer n~(2\le n\le 20000) and two different integers a and b.

Output

For each test case, output the winner (``Yuwgna" or ``Iaka"). Both of them will make the best possible decision each time.

Sample Input

162 1 23 1 367 1 2100 1 28 6 89 6 810 6 811 6 812 6 813 6 814 6 815 6 816 6 81314 6 81994 1 131994 7 12

Sample Output

Case #1: IakaCase #2: YuwgnaCase #3: YuwgnaCase #4: IakaCase #5: IakaCase #6: IakaCase #7: YuwgnaCase #8: YuwgnaCase #9: IakaCase #10: IakaCase #11: YuwgnaCase #12: YuwgnaCase #13: IakaCase #14: YuwgnaCase #15: IakaCase #16: Iaka

题意：n座塔，除编号为a，b的塔保留下来以外，其他塔需要重建，对于已建成的塔j，k(包括a，b两塔)，每次只能重建编号为j+k或j-k的塔，Yuwgna和Iaka两个僧人轮流建一座塔，Yuwgna先手，最后不能建的人输，问最终获胜的人是哪个

#include<stdio.h>#include<algorithm>using namespace std;int fun(int x,int y){int z = y-x;if(z == x)return z;if(z > x)swap(x,z);return fun(z,x); }int n,a,b;int main(){int t,text = 1;scanf("%d",&t);while(t--){scanf("%d%d%d",&n,&a,&b);if(a>b)swap(a,b);int m = fun(a,b);int cnt = n/m-2;printf("Case #%d: %s\n",text++,cnt%2 ==0?"Iaka":"Yuwgna");}return 0;}