Chef has a sequence $A_1, A_2, \ldots, A_N$; each element of this sequence is either $0$ or $1$. Appy gave him a string $S$ with length $Q$ describing a sequence of queries. There are two types of queries:
- '!': right-shift the sequence $A$, i.e. replace $A$ by another sequence $B_1, B_2, \ldots, B_N$ satisfying $B_{i+1} = A_i$ for each valid $i$ and $B_1 = A_N$
- '?': find the length of the longest contiguous subsequence of $A$ with length $\le K$ such that each element of this subsequence is equal to $1$
Answer all queries of the second type.

-----Input-----
- The first line of the input contains three space-separated integers $N$, $Q$ and $K$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.
- The third line contains a string with length $Q$ describing queries. Each character of this string is either '?', denoting a query of the second type, or '!', denoting a query of the first type.

-----Output-----
For each query of the second type, print a single line containing one integer — the length of the longest required subsequence.

-----Constraints-----
- $1 \le K \le N \le 10^5$
- $1 \le Q \le 3 \cdot 10^5$
- $0 \le A_i \le 1$ for each valid $i$
- $S$ contains only characters '?' and '!'

-----Subtasks-----
Subtask #1 (30 points):
- $1 \le N \le 10^3$
- $1 \le Q \le 3 \cdot 10^3$
Subtask #2 (70 points): original constraints 

-----Example Input-----
5 5 3
1 1 0 1 1
?!?!?    

-----Example Output-----
2
3
3

-----Explanation-----
- In the first query, there are two longest contiguous subsequences containing only $1$-s: $A_1, A_2$ and $A_4, A_5$. Each has length $2$.
- After the second query, the sequence $A$ is $[1, 1, 1, 0, 1]$.
- In the third query, the longest contiguous subsequence containing only $1$-s is $A_1, A_2, A_3$.
- After the fourth query, $A = [1, 1, 1, 1, 0]$.
- In the fifth query, the longest contiguous subsequence containing only $1$-s is $A_1, A_2, A_3, A_4$ with length $4$. However, we only want subsequences with lengths $\le K$. One of the longest such subsequences is $A_2, A_3, A_4$, with length $3$.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "n,q,k = map(int, input().split())\na = [int(x) for x in input().split()]\ns = input()\nm = 0\nl = 0\nfor i in a:\n if i==1:\n  m += 1\n else:\n  m = 0\n if m>=k:\n  l = k\n  break\n elif m>l:\n  l = m\nfor i in s:\n if i == '?':\n  print(l)\n else:\n  a.insert(0,a[n-1])\n  a.pop()\n  if a[0]!=0:\n   m = 0\n   l = 0\n   for j in a:\n    if j==1:\n     m += 1\n    else:\n     m = 0\n    if m>=k:\n     l = k\n     break\n    elif m>l:\n     l = m"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13247