# Practice on Toph

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## Interesting Subarray

You will be given an array **A** of length **N** and two more integers **K** and **X**. You have to find the length of the largest interesting sub-array inside the array **A**.

A sub-array is called interesting if the following two conditions are satisfied.

- The largest element in that sub-array is
**K**. - The number of occurrences of
**K**in that sub-array is at least**X**.

Find the maximum length of a sub-array which is called interesting.

### Input

The first line of the input contains a single integer **T** which denotes the number of test cases. The first line of a test case contains three integers **N**, **K** and **X**. The next line of the test case contains **N** space separated integers denoting the elements of the array **A**.

#### Constraints

`${1 \leq T \leq 10}$`

`${1 \leq N \leq 50000}$`

`${1 \leq X \leq N}$`

`${1 \leq A_{i}, K \leq 1000000}$`

### Output

For each of the test cases, print the result in a single line. If there’s no valid interesting sub-array then print **-1**.

### Samples

Input | Output |
---|---|

2 8 6 2 6 2 6 3 8 2 1 6 12 6 2 6 2 6 8 2 1 6 6 4 6 9 3 | 4 6 |

In the first test case of the sample I/O, the largest interesting sub-array starts at index **1** and ends at index **4** (1 based indexing). In this sub-array, **6** occurs **2** times (which is >= X) and **6** is the largest element, so it’s an interesting sub-array. No other interesting sub-array has length greater than **4**.