Problem Statement

A preliminary round of a quiz competition was held. There are $N$ participants, numbered $1$ to $N$, and at most $M$ of them can pass the preliminary round.

The preliminary round consists of $K$ two-choice quiz questions, and the answer to each question is o or x. Participant $i$'s answer to the $j$-th question is given as the $j$-th character of the string $S_i$. The correct answer to the $j$-th question is given as the $j$-th character of the string $T$.

The qualifiers are determined by the following procedure.

• Initially, the numbers of qualifiers and non-qualifiers are both $0$; all $N$ participants are undetermined.
• For $k=1,2,\dots,K$ in this order, perform the following process.
  • If the number of qualifiers plus the number of undetermined participants who answered the $k$-th question correctly is at most $M$, then all undetermined participants who answered the $k$-th question correctly become qualifiers.
  • Otherwise, all undetermined participants who answered the $k$-th question incorrectly become non-qualifiers.
• All remaining undetermined participants become non-qualifiers.

You are given $Q$ queries in the following format. Process them in order.

• Integers $i$ and $j$ are given. Change participant $i$'s answer to the $j$-th question from o to x, or from x to o. Then, determine whether participant $i$ passes the preliminary round.

The change of the answer in each query remains in effect when processing subsequent queries as well.

Constraints

• $1 \leq M \leq N \leq 3\times 10^4$
• $1 \leq K \leq 200$
• $S_i$ and $T$ are strings of length $K$ consisting of o and x.
• $1 \leq Q \leq 5\times 10^4$
• For each query, $1\leq i \leq N$ and $1 \leq j \leq K$.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

• $N$ $M$ $K$
• $T$
• $S_1$
• $\vdots$
• $S_N$
• $Q$
• $\mathrm{query}_1$
• $\vdots$
• $\mathrm{query}_Q$

Here, $\mathrm{query}_q$ represents the $q$-th query, and is given in the following format:

• $i$ $j$

Output

Output $Q$ lines. The $q$-th line should contain Yes if the participant specified in the $q$-th query passes the preliminary round, and No otherwise.

5 3 3
oxo
oxo
oxx
xxo
xox
xoo
3
5 1
1 3
4 1

Yes
Yes
No

• Before the first query, participants $1,2$ pass on the first question and participant $3$ passes on the second question, so the qualifiers are the three participants $1,2,3$.
• After the first query, participants $1,2,5$ pass on the first question, so the qualifiers are the three participants $1,2,5$. Since participant $5$ passes the preliminary round, output Yes.
• After the second query, participants $1,2,5$ still pass on the first question, so the qualifiers are the three participants $1,2,5$. Since participant $1$ passes the preliminary round, output Yes.
• After the third query, participant $3$ is eliminated on the first question, participants $1,2$ pass on the second question, and participant $5$ passes on the third question, so the qualifiers remain the three participants $1,2,5$. Since participant $4$ does not pass the preliminary round, output No.

3 1 2
ox
xo
oo
ox
4
3 1
1 1
2 2
1 2

No
No
Yes
No

1 1 1
o
o
2
1 1
1 1

No
Yes

• Source: AtCoder ABC 475 E