#P1290. Canbethechampion?

Canbethechampion?

There are 2^n athletes have a match for the champion. each people have a ability assessment that number 1、2、3……2^n.(according to the ability rank) the compition like this: each two athlets will have a match.the winner will continue with other winner until finding the champion.(it means that if there are 2^n athletes have the match.then 2^(n-1) will remain.then 2^(n-2) will remain …… the end only one people remain. he is the champion ). but sometime may be the athlete whose number lower can defeat athlete whose number is high. now I tell you  the athlete of number j may be defeat athlete number from (j-k) to last.

To the first example ,the number 7 can defeat number 5 to 8, number 6 can defeat number 4 to 8, number 5 can defeat number 3 to 8......
Can you tell me if the athlete number m can be the champion ?

Input

multiunit cases .first line is the number of case T(T<150); then each line have three integar indicate the n,m,k;(n<=12;m<=2^n;0=<k<=2^31;)

Output

first line is the case number like "Case : 1" .next line if the bility of m can be champion ,printf YES,or NO;

Sample Input

2
3 7 2
3 7 3

Sample Output

Case : 1
NO
Case : 2
YES

HINT

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