You are given a string $$$s$$$ consisting of characters A and B.

Your task is to split it into blocks of length $$$1$$$ and $$$2$$$ in such a way that

there are no more than $$$a$$$ strings equal to "A";
there are no more than $$$b$$$ strings equal to "B";
there are no more than $$$ab$$$ strings "AB";
there are no more than $$$ba$$$ strings "BA";

Strings "AA" and "BB" are prohibited. Each character of the initial string $$$s$$$ should belong to exactly one block.

Input

The first line contains one integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. Next, $$$t$$$ independent cases follow.

The first line of each test case contains a single string $$$s$$$ ($$$1 \le |s| \le 5 \cdot 10^5$$$) consisting only of characters A and/or B.

The second line of each test case contains four integers $$$a$$$, $$$b$$$, $$$ab$$$, and $$$ba$$$ ($$$0 \le a, b, ab, ba \le 5 \cdot 10^5$$$) — the maximum allowed number of strings "A", "B", "AB", and "BA" correspondingly.

It's guaranteed that the total length of $$$s$$$ doesn't exceed $$$5 \cdot 10^5$$$ over all test cases.

Output

For each test case, print YES if it's possible to split string $$$s$$$. Otherwise, print NO.

Note

In the third test case, all possible splits are: A|B|A, AB|A or A|BA. All of them have at least one "A".

In the fourth test case, one of the possible splits is the following: A|B|B|A|B|A|A|B.

In the fifth test case, one of the possible splits is the following: A|BA|B|BA|AB|BA|AB.

A, B, AB and BA

Examples