CF1729F.Kirei and the Linear Function

Given the string $s$ of decimal digits (0-9) of length $n$ .

A substring is a sequence of consecutive characters of a string. The substring of this string is defined by a pair of indexes — with its left and right ends. So, each pair of indexes ( $l, r$ ), where $1 \le l \le r \le n$ , corresponds to a substring of the string $s$ . We will define as $v(l,r)$ the numeric value of the corresponding substring (leading zeros are allowed in it).

For example, if $n=7$ , $s=$ "1003004", then $v(1,3)=100$ , $v(2,3)=0$ and $v(2,7)=3004$ .

You are given $n$ , $s$ and an integer $w$ ( $1 \le w < n$ ).

You need to process $m$ queries, each of which is characterized by $3$ numbers $l_i, r_i, k_i$ ( $1 \le l_i \le r_i \le n; 0 \le k_i \le 8$ ).

The answer to the $i$ th query is such a pair of substrings of length $w$ that if we denote them as $(L_1, L_1+w-1)$ and $(L_2, L_2+w-1)$ , then:

• $L_1 \ne L_2$ , that is, the substrings are different;
• the remainder of dividing a number $v(L_1, L_1+w-1) \cdot v(l_i, r_i) + v(L_2, L_2 + w - 1)$ by $9$ is equal to $k_i$ .

If there are many matching substring pairs, then find a pair where $L_1$ is as small as possible. If there are many matching pairs in this case, then minimize $L_2$ .

Note that the answer may not exist.

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

The first line of each test case contains a string $s$ , which contains only the characters 0-9 and has a length $n$ ( $2 \le n \le 2 \cdot 10^5$ ).

The second line contains two integers $w, m$ ( $1 \le w < n, 1 \le m \le 2 \cdot 10^5$ ), where $n$ — is the length of the given string $s$ . The number $w$ denotes the lengths of the substrings being searched for, and $m$ is the number of queries to be processed.

The following $m$ lines contain integers $l_i, r_i, k_i$ ( $1 \le l_i \le r_i \le n$ , $0 \le k_i \le 8$ ) — $i$ th query parameters.

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

For each request, print in a separate line:

• left borders of the required substrings: $L_1$ and $L_2$ ;
• -1 -1 otherwise, if there is no solution.

If there are several solutions, minimize $L_1$ first, and minimize $L_2$ second.

Consider the first test case of example inputs. In this test case $n=7$ , $s=$ "1003004", $w=4$ and one query $l_1=1$ , $r_1=2$ , $k_1=1$ . Note that $v(1,2)=10$ . We need to find a pair of substrings of length $4$ such that $v(L_1, L_1+3)\cdot10+v(L_2,L_2+3)$ has a remainder of $k_1=1$ when divided by $9$ . The values $L_1=2, L_2=4$ actually satisfy all the requirements: $v(L_1, L_1+w-1)=v(2,5)=30$ , $v(L_2, L_2+w-1)=v(4,7)=3004$ . Indeed, $30\cdot10+3004=3304$ , which has a remainder of $1$ when divided by $9$ . It can be shown that $L_1=2$ is the minimum possible value, and $L_2=4$ is the minimum possible with $L_1=2$ .