Strong Password
Description
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.
Input
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 $3 \cdot 10^5$.
Output
For each testcase, print "YES" if there exists a password that fits all criteria. Print "NO" otherwise.
5
88005553535123456
2
50
56
123412341234
3
111
444
1234
4
4321
4321
459
2
49
59
00010
2
10
11
YES
NO
YES
NO
YES
Note
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".