This documentation is automatically generated by online-judge-tools/verification-helper
import cp_library.__header__
from cp_library.misc.typing import _T
from typing import Generic, Union, Callable, Optional
import cp_library.ds.__header__
import cp_library.ds.tree.__header__
import cp_library.ds.tree.bit.__header__
class BITBase(Generic[_T]):
_lst = list
K: int = 1
def __init__(bit, v: Union[int, list[_T]], e: _T = None) -> None:
if isinstance(v, int):
bit._n = v
if bit._lst is list:
bit._d = [e]*v if e is not None else [0]*v
elif e is not None:
bit._d = bit._lst(*([e_]*v for e_ in e))
else:
bit._d = bit._lst(*([0]*v for _ in range(bit.K)))
else:
bit.build(v)
bit.e = e if e is not None else (0 if bit._lst is list else tuple(0 for _ in range(bit.K)))
bit._lb = 1 << bit._n.bit_length()
def build(bit, data: list[_T]):
bit._n = len(data)
if bit._lst is list:
bit._d = bit._lst(data)
else:
bit._d = bit._lst(*([data[i][j] for i in range(len(data))] for j in range(len(data[0]))))
for i in range(bit._n):
if (r := i | i + 1) < bit._n:
bit._add(r, bit._d[i])
def _add(bit, i: int, x: _T) -> None:
bit._d[i] = bit._op(bit._d[i], x)
def _op(bit, a: _T, b: _T) -> _T:
return a + b
def _sub(bit, a: _T, b: _T) -> _T:
return a - b
def add(bit, i: int, x: _T) -> None:
while i < bit._n: bit._add(i, x); i |= i + 1
def sum(bit, n: int) -> _T:
s = bit.e
while n: s, n = bit._op(s, bit._d[n - 1]), n & n - 1
return s
def sum_range(bit, l: int, r: int) -> _T:
s = bit.e
while r: s, r = bit._op(s, bit._d[r - 1]), r & r - 1
while l: s, l = bit._sub(s, bit._d[l - 1]), l & l - 1
return s
def __len__(bit) -> int: return bit._n
def __getitem__(bit, i: int) -> _T:
s, l = bit._d[i], i & (i + 1)
while l != i: s, i = bit._sub(s, bit._d[i - 1]), i - (i & -i)
return s
get = __getitem__
def __setitem__(bit, i: int, x: _T) -> None:
bit.add(i, bit._sub(x, bit[i]))
set = __setitem__
def prelist(bit) -> list[_T]:
pre = [bit.e] + bit._d[:] if bit._lst is list else bit._lst(*([e_] * (bit._n + 1) for e_ in bit.e))
for i in range(bit._n): pre[i+1] = bit._d[i]
for i in range(bit._n + 1):
if i & i - 1 < bit._n + 1:
pre[i] = bit._op(pre[i], pre[i & i - 1])
return pre
def bisect_left(bit, v, key: Optional[Callable] = None) -> int:
i = 0
s = bit.e
if v <= s: return -1
m = bit._lb
if key:
while m := m >> 1:
if (ni := m | i) <= bit._n and key(ns := bit._op(s, bit._d[ni - 1])) < v:
s, i = ns, ni
else:
while m := m >> 1:
if (ni := m | i) <= bit._n and (ns := bit._op(s, bit._d[ni - 1])) < v:
s, i = ns, ni
return i
def bisect_right(bit, v, key: Optional[Callable] = None) -> int:
i = 0
s = bit.e
m = bit._lb
if key:
while m := m >> 1:
if (ni := m | i) <= bit._n and key(ns := bit._op(s, bit._d[ni - 1])) <= v:
s, i = ns, ni
else:
while m := m >> 1:
if (ni := m | i) <= bit._n and (ns := bit._op(s, bit._d[ni - 1])) <= v:
s, i = ns, ni
return i
'''
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
https://kobejean.github.io/cp-library
'''
from typing import TypeVar
_S = TypeVar('S'); _T = TypeVar('T'); _U = TypeVar('U'); _T1 = TypeVar('T1'); _T2 = TypeVar('T2'); _T3 = TypeVar('T3'); _T4 = TypeVar('T4'); _T5 = TypeVar('T5'); _T6 = TypeVar('T6')
from typing import Generic, Union, Callable, Optional
'''
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ 7 ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┯━┛
┏━━━━━━━━━━━━━━━━━━┓ │
┃ 3 ┃◄────────────────┤
┗━━━━━━━━━━━━━━━━┯━┛ │
┏━━━━━━━━┓ │ ┏━━━━━━━━┓ │
┃ 1 ┃◄──────┤ ┃ 5 ┃◄──────┤
┗━━━━━━┯━┛ │ ┗━━━━━━┯━┛ │
┏━━━┓ │ ┏━━━┓ │ ┏━━━┓ │ ┏━━━┓ │
┃ 0 ┃◄─┤ ┃ 2 ┃◄─┤ ┃ 4 ┃◄─┤ ┃ 6 ┃◄─┤
┗━┯━┛ │ ┗━┯━┛ │ ┗━┯━┛ │ ┗━┯━┛ │
│ │ │ │ │ │ │ │
▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼
┏━━━┓┏━━━┓┏━━━┓┏━━━┓┏━━━┓┏━━━┓┏━━━┓┏━━━┓
┃ 0 ┃┃ 1 ┃┃ 2 ┃┃ 3 ┃┃ 4 ┃┃ 5 ┃┃ 6 ┃┃ 7 ┃
┗━━━┛┗━━━┛┗━━━┛┗━━━┛┗━━━┛┗━━━┛┗━━━┛┗━━━┛
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
Data Structure - Tree - Binary Index Tree
'''
class BITBase(Generic[_T]):
_lst = list
K: int = 1
def __init__(bit, v: Union[int, list[_T]], e: _T = None) -> None:
if isinstance(v, int):
bit._n = v
if bit._lst is list:
bit._d = [e]*v if e is not None else [0]*v
elif e is not None:
bit._d = bit._lst(*([e_]*v for e_ in e))
else:
bit._d = bit._lst(*([0]*v for _ in range(bit.K)))
else:
bit.build(v)
bit.e = e if e is not None else (0 if bit._lst is list else tuple(0 for _ in range(bit.K)))
bit._lb = 1 << bit._n.bit_length()
def build(bit, data: list[_T]):
bit._n = len(data)
if bit._lst is list:
bit._d = bit._lst(data)
else:
bit._d = bit._lst(*([data[i][j] for i in range(len(data))] for j in range(len(data[0]))))
for i in range(bit._n):
if (r := i | i + 1) < bit._n:
bit._add(r, bit._d[i])
def _add(bit, i: int, x: _T) -> None:
bit._d[i] = bit._op(bit._d[i], x)
def _op(bit, a: _T, b: _T) -> _T:
return a + b
def _sub(bit, a: _T, b: _T) -> _T:
return a - b
def add(bit, i: int, x: _T) -> None:
while i < bit._n: bit._add(i, x); i |= i + 1
def sum(bit, n: int) -> _T:
s = bit.e
while n: s, n = bit._op(s, bit._d[n - 1]), n & n - 1
return s
def sum_range(bit, l: int, r: int) -> _T:
s = bit.e
while r: s, r = bit._op(s, bit._d[r - 1]), r & r - 1
while l: s, l = bit._sub(s, bit._d[l - 1]), l & l - 1
return s
def __len__(bit) -> int: return bit._n
def __getitem__(bit, i: int) -> _T:
s, l = bit._d[i], i & (i + 1)
while l != i: s, i = bit._sub(s, bit._d[i - 1]), i - (i & -i)
return s
get = __getitem__
def __setitem__(bit, i: int, x: _T) -> None:
bit.add(i, bit._sub(x, bit[i]))
set = __setitem__
def prelist(bit) -> list[_T]:
pre = [bit.e] + bit._d[:] if bit._lst is list else bit._lst(*([e_] * (bit._n + 1) for e_ in bit.e))
for i in range(bit._n): pre[i+1] = bit._d[i]
for i in range(bit._n + 1):
if i & i - 1 < bit._n + 1:
pre[i] = bit._op(pre[i], pre[i & i - 1])
return pre
def bisect_left(bit, v, key: Optional[Callable] = None) -> int:
i = 0
s = bit.e
if v <= s: return -1
m = bit._lb
if key:
while m := m >> 1:
if (ni := m | i) <= bit._n and key(ns := bit._op(s, bit._d[ni - 1])) < v:
s, i = ns, ni
else:
while m := m >> 1:
if (ni := m | i) <= bit._n and (ns := bit._op(s, bit._d[ni - 1])) < v:
s, i = ns, ni
return i
def bisect_right(bit, v, key: Optional[Callable] = None) -> int:
i = 0
s = bit.e
m = bit._lb
if key:
while m := m >> 1:
if (ni := m | i) <= bit._n and key(ns := bit._op(s, bit._d[ni - 1])) <= v:
s, i = ns, ni
else:
while m := m >> 1:
if (ni := m | i) <= bit._n and (ns := bit._op(s, bit._d[ni - 1])) <= v:
s, i = ns, ni
return i