A13334. Homecoming

After a long party Petya decided to return home, but he turned out to be at the opposite end of the town from his home. There are $n$ crossroads in the line in the town, and there is either the bus or the tram station at each crossroad.

The crossroads are represented as a string $s$ of length $n$ , where $s_i = \texttt{A}$ , if there is a bus station at $i$ -th crossroad, and $s_i = \texttt{B}$ , if there is a tram station at $i$ -th crossroad. Currently Petya is at the first crossroad (which corresponds to $s_1$ ) and his goal is to get to the last crossroad (which corresponds to $s_n$ ).

If for two crossroads $i$ and $j$ for all crossroads $i, i+1, \ldots, j-1$ there is a bus station, one can pay $a$ roubles for the bus ticket, and go from $i$ -th crossroad to the $j$ -th crossroad by the bus (it is not necessary to have a bus station at the $j$ -th crossroad). Formally, paying $a$ roubles Petya can go from $i$ to $j$ if $s_t = \texttt{A}$ for all $i \le t < j$ .

If for two crossroads $i$ and $j$ for all crossroads $i, i+1, \ldots, j-1$ there is a tram station, one can pay $b$ roubles for the tram ticket, and go from $i$ -th crossroad to the $j$ -th crossroad by the tram (it is not necessary to have a tram station at the $j$ -th crossroad). Formally, paying $b$ roubles Petya can go from $i$ to $j$ if $s_t = \texttt{B}$ for all $i \le t < j$ .

For example, if $s$ ="AABBBAB", $a=4$ and $b=3$ then Petya needs:

- buy one bus ticket to get from $1$ to $3$ ,
- buy one tram ticket to get from $3$ to $6$ ,
- buy one bus ticket to get from $6$ to $7$ .

Thus, in total he needs to spend $4+3+4=11$ roubles. Please note that the type of the stop at the last crossroad (i.e. the character $s_n$ ) does not affect the final expense.

Now Petya is at the first crossroad, and he wants to get to the $n$ -th crossroad. After the party he has left with $p$ roubles. He's decided to go to some station on foot, and then go to home using only public transport.

Help him to choose the closest crossroad $i$ to go on foot the first, so he has enough money to get from the $i$ -th crossroad to the $n$ -th, using only tram and bus tickets.

Each test contains one or more test cases. The first line contains the number of test cases $t$ ( $1 \le t \le 10^4$ ).

The first line of each test case consists of three integers $a, b, p$ ( $1 \le a, b, p \le 10^5$ ) — the cost of bus ticket, the cost of tram ticket and the amount of money Petya has.

The second line of each test case consists of one string $s$ , where $s_i = \texttt{A}$ , if there is a bus station at $i$ -th crossroad, and $s_i = \texttt{B}$ , if there is a tram station at $i$ -th crossroad ( $2 \le |s| \le 10^5$ ).

It is guaranteed, that the sum of the length of strings $s$ by all test cases in one test doesn't exceed $10^5$ .

For each test case print one number — the minimal index $i$ of a crossroad Petya should go on foot. The rest of the path (i.e. from $i$ to $n$ he should use public transport).