The Next

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)

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Description

Let $L$ denote the number of 1s in integer $D$’s binary representation. Given two integers $S_1$ and $S_2$, we call $D$ a WYH number if $S_1≤L≤S_2$.
With a given $D$, we would like to find the next WYH number $Y$, which is JUST larger than $D$. In other words, $Y$ is the smallest WYH number among the numbers larger than $D$. Please write a program to solve this problem.

Input

The first line of input contains a number $T$ indicating the number of test cases ($T≤300000$).
Each test case consists of three integers $D$, $S_1$, and $S_2$, as described above. It is guaranteed that $0≤D<2^{31}$ and $D$ is a WYH number.

Output

For each test case, output a single line consisting of “Case #X: Y”. $X$ is the test case number starting from 1. $Y$ is the next WYH number.

Sample Input

3 11 2 4 22 3 3 15 2 5

Sample Output

Case #1: 12 Case #2: 25 Case #3: 17

Hint

wange2014

Source

2015 ACM/ICPC Asia Regional Hefei Online

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