HDU5512--Pagodas

Problem 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≤a≠b≤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∉{a,b} and 1≤i≤n) if there exist two pagodas standing erect, labelled j and k respectively, 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≤t≤500) which is the number of test cases.
For each test case, the first line provides the positive integer n (2≤n≤20000) and two different integers a and b.

Output
For each test case, output the winner (Yuwgna" orIaka”). Both of them will make the best possible decision each time.

Sample Input

16
2 1 2
3 1 3
67 1 2
100 1 2
8 6 8
9 6 8
10 6 8
11 6 8
12 6 8
13 6 8
14 6 8
15 6 8
16 6 8
1314 6 8
1994 1 13
1994 7 12

Sample Output

Case #1: Iaka
Case #2: Yuwgna
Case #3: Yuwgna
Case #4: Iaka
Case #5: Iaka
Case #6: Iaka
Case #7: Yuwgna
Case #8: Yuwgna
Case #9: Iaka
Case #10: Iaka
Case #11: Yuwgna
Case #12: Yuwgna
Case #13: Iaka
Case #14: Yuwgna
Case #15: Iaka
Case #16: Iaka
题目大意：给你三个数n,a,b 有n个塔然后标号为1~n，标号为a，b的塔还存在其他的都不存在，现在让你重建标号为i的塔，要满足1<=i<=n而且i不为a也不为b。
Yuwgna先建塔，所有的塔都只能重建1次，谁先没塔可建，谁就输了。

题目解析：设gcd（a，b）=c。a=kc，b=pc，1~n中为c的倍数的标号就能建，所以找出其中为c的倍数的数的个数 如果为2的倍数Iaka赢，否则Yuwgna赢。
为什么是这样的感觉就是题感，多写几组数据发现有此规律。
刚开始的时候思路错了做了好久都没做对。
AC代码：

#include <cstdio>using namespace std;int gcd(int a, int b){    if(b == 0)        return a;    return gcd(b, a % b);}int main(){    int t, a, b, n;    scanf("%d", &t);    for(int ca = 1; ca <= t; ca++)    {        scanf("%d%d%d", &n, &a, &b);        int k = gcd(a, b);        if((n/k)%2==0)        {            printf("Case #%d: Iaka\n", ca);        }        else        {            printf("Case #%d: Yuwgna\n", ca);        }    }    return 0;}