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### Problem

### Input

### Output

### Limits

#### Small dataset

#### Large dataset

### Sample

I have a sequence of **N** binary digits. I am looking for a
substring with just the right proportion of 0s and 1s, but it may not
exist, so I will settle for something that's just pretty good.

Can you find a substring where the fraction of 1s is as close as possible to the given fraction **F**? Output the earliest possible index at which such a substring starts.

The first line of the input gives the number of test cases, **T**. **T** test cases follow. Each one starts with a line containing **N** and **F**. **F** will be a decimal fraction between 0 and 1 inclusive, with exactly 6 digits after the decimal point. The next line contains **N** digits, each being either 0 or 1.

For each test case, output one line containing "Case #x: y", where x is
the test case number (starting from 1) and y is the 0-based index of the
start of the substring with the fraction of 1s that is as close as
possible to **F**. If there are multiple possible answers, output the smallest correct value.

1 ≤ **T** ≤ 100.

0 ≤ **F** ≤ 1**F** will have exactly 6 digits after the decimal point.

1 ≤ **N** ≤ 1000.

1 ≤ **N** ≤ 500,000.

Input |
Output |

5 12 0.666667 001001010111 11 0.400000 10000100011 9 0.000000 111110111 5 1.000000 00000 15 0.333333 000000000011000 |
Case #1: 5 Case #2: 5 Case #3: 5 Case #4: 0 Case #5: 6 |

In Case #1, there is no substring that has exactly a 1-proportion of exactly