CF1845C.Strong Password

Monocarp finally got the courage to register on ForceCoders. He came up with a handle but is still thinking about the password.

He wants his password to be as strong as possible, so he came up with the following criteria:

• the length of the password should be exactly $m$ ;
• the password should only consist of digits from $0$ to $9$ ;
• the password should not appear in the password database (given as a string $s$ ) as a subsequence (not necessarily contiguous).

Monocarp also came up with two strings of length $m$ : $l$ and $r$ , both consisting only of digits from $0$ to $9$ . He wants the $i$ -th digit of his password to be between $l_i$ and $r_i$ , inclusive.

Does there exist a password that fits all criteria?

The first line contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of testcases.

The first line of each testcase contains a string $s$ ( $1 \le |s| \le 3 \cdot 10^5$ ), consisting only of digits from $0$ to $9$ — the password database.

The second line contains a single integer $m$ ( $1 \le m \le 10$ ) — the required length of the password.

The third line contains a string $l$ ( $|l| = m$ ), consisting only of digits from $0$ to $9$ — the lower restriction on each digit.

The fourth line contains a string $r$ ( $|r| = m$ ), consisting only of digits from $0$ to $9$ — the upper restriction on each digit. $l_i \le r_i$ for all $i$ from $1$ to $m$ .

The sum of lengths of $s$ over all testcases doesn't exceed $3 \cdot 10^5$ .

For each testcase, print "YES" if there exists a password that fits all criteria. Print "NO" otherwise.

In the first testcase, Monocarp can choose password "50". It doesn't appear in $s$ as a subsequence.

In the second testcase, all combinations of three digits, each of them being from $1$ to $4$ , fit the criteria on $l$ and $r$ . However, all of them appear in $s$ as subsequences. For example, "314" appears at positions $[3, 5, 12]$ and "222" appears at positions $[2, 6, 10]$ .

In the third testcase, Monocarp can choose password "4321". Actually, that is the only password that fits the criteria on $l$ and $r$ . Luckily, it doesn't appear in $s$ as a subsequence.

In the fourth testcase, only "49" and "59" fit the criteria on $l$ and $r$ . Both of them appear in $s$ as subsequences.

In the fifth testcase, Monocarp can choose password "11".