B. Expansion Plan 2
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
ak+q - over the crimson skies
⠀

You are analyzing an infinite grid with coordinates $$$(X, Y)$$$ (specifically, the cell immediately above $$$(0, 0)$$$ is $$$(0, 1)$$$, and the cell immediately on the right of $$$(0, 0)$$$ is $$$(1, 0)$$$). Initially, only the cell at $$$(0, 0)$$$ is black.

You are given a string $$$a_1a_2 \ldots a_n$$$ of length $$$n$$$ consisting of characters $$$\texttt{"4"}$$$ and $$$\texttt{"8"}$$$, which describes $$$n$$$ expansion operations. For each $$$i$$$ from $$$1$$$ to $$$n$$$, the following happens for all cells simultaneously:

  • if $$$s_i = \texttt{"4"}$$$: for each cell, if it is orthogonally adjacent to a black cell (i.e., it shares a side), it becomes black; otherwise, its state remains the same;
  • if $$$s_i = \texttt{"8"}$$$: for each cell, if it is orthogonally or diagonally adjacent to a black cell (i.e, it shares a side or a corner), it becomes black; otherwise, its state remains the same.

Is the cell $$$(x, y)$$$ black at the end of the process?

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains three integers $$$n$$$, $$$x$$$, $$$y$$$ ($$$1 \le n \le 2 \cdot 10^5, -10^9 \le x, y \le 10^9$$$) — the number of expansion operations, and the $$$x$$$ and $$$y$$$ coordinates of the cell you are interested in, respectively.

The second line of each test case contains a string $$$s$$$ of length $$$n$$$ consisting of characters $$$\texttt{"4"}$$$ and $$$\texttt{"8"}$$$ — the types of expansion operations.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output $$$\texttt{YES}$$$ if the cell $$$(x, y)$$$ is black after the expansion operations described by the string $$$s$$$, and $$$\texttt{NO}$$$ otherwise.

The judge is case-insensitive (for example, $$$\texttt{YES}$$$, $$$\texttt{Yes}$$$, $$$\texttt{yes}$$$, $$$\texttt{yEs}$$$ will all be recognized as positive answers).

Example
Input
6
3 3 3
888
4 5 1
4884
4 3 -3
4884
7 -7 -5
4884884
10 0 0
4884884888
1 1 1
4
Output
YES
NO
YES
NO
YES
NO
Note

The first three test cases are illustrated below:

In the first test case, after the expansion operations in the string $$$\texttt{"888"}$$$, cell $$$(3, 3)$$$ is black, so the answer is $$$\texttt{YES}$$$.

In the second test case, cell $$$(5, 1)$$$ is white after the expansion operations in the string $$$\texttt{"4884"}$$$.