This documentation is automatically generated by online-judge-tools/verification-helper
# verification-helper: PROBLEM https://judge.yosupo.jp/problem/point_set_range_composite_large_array
def main():
mod = 998244353
shift, mask = 30, (1<<30)-1
N, Q = read()
TreapMonoid.reserve(1+2*Q)
def op(a,b):
ac, ad = pack_dec(a, shift, mask)
bc, bd = pack_dec(b, shift, mask)
return pack_enc(ac*bc%mod, (ad*bc+bd)%mod, shift)
T = TreapMonoid(op, 1<<shift)
D = {}
for _ in range(Q):
t, *q = read()
if t == 0:
p, c, d = q
# T[p] = pack_enc(c, d, shift)
T[p] = D[p] = pack_enc(c, d, shift)
else:
l, r, x = q
# a, b = pack_dec(T.prod(l,r), shift, mask)
a, b = pack_dec(T[l:r], shift, mask)
write((a*x+b)%mod)
# test if the following can be run in reasonable time
for key in D:
assert T[key] == D[key]
for i, key in enumerate(D):
assert key in T
del T[key]
assert key not in T
if i%10000 == 0: T._v()
# addition of duplicate keys/values
for p in range(Q): T.insert(0, 0)
from cp_library.ds.tree.bst.treap_monoid_cls import TreapMonoid
from cp_library.bit.pack.pack_enc_fn import pack_enc
from cp_library.bit.pack.pack_dec_fn import pack_dec
from cp_library.io.read_fn import read
from cp_library.io.write_fn import write
if __name__ == '__main__':
main()
# verification-helper: PROBLEM https://judge.yosupo.jp/problem/point_set_range_composite_large_array
def main():
mod = 998244353
shift, mask = 30, (1<<30)-1
N, Q = read()
TreapMonoid.reserve(1+2*Q)
def op(a,b):
ac, ad = pack_dec(a, shift, mask)
bc, bd = pack_dec(b, shift, mask)
return pack_enc(ac*bc%mod, (ad*bc+bd)%mod, shift)
T = TreapMonoid(op, 1<<shift)
D = {}
for _ in range(Q):
t, *q = read()
if t == 0:
p, c, d = q
# T[p] = pack_enc(c, d, shift)
T[p] = D[p] = pack_enc(c, d, shift)
else:
l, r, x = q
# a, b = pack_dec(T.prod(l,r), shift, mask)
a, b = pack_dec(T[l:r], shift, mask)
write((a*x+b)%mod)
# test if the following can be run in reasonable time
for key in D:
assert T[key] == D[key]
for i, key in enumerate(D):
assert key in T
del T[key]
assert key not in T
if i%10000 == 0: T._v()
# addition of duplicate keys/values
for p in range(Q): T.insert(0, 0)
'''
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
https://kobejean.github.io/cp-library
'''
def reserve(A: list, est_len: int) -> None: ...
try:
from __pypy__ import resizelist_hint
except:
def resizelist_hint(A: list, est_len: int):
pass
reserve = resizelist_hint
i64_max = (1<<63)-1
class BST:
__slots__ = 'r'
K,sub,st=[-1],[-1,-1],[]
def __init__(T):T.r=T._nr()
def _nt(T):return T.__class__()
def _nr(T):r=len(T.K);T.K.append(i64_max);T.sub.append(-1);T.sub.append(-1);return r
def _nn(T,k):n=len(T.K);T.K.append(k);T.sub.append(-1);T.sub.append(-1);return n
def insert(T,k):T._i(T.r<<1,k,n:=T._nn(k));T._r();return n
def get(T,k):
if~(i:=T._f(T.r<<1,k)):return i
raise KeyError
def pop(T,k):
if ~(i:=T._t(T.r<<1,k)):T._d(i,T.st[-1]);T._r();return i
else:T.st.clear();raise KeyError
def __delitem__(T,k):
if~(i:=T._t(T.r<<1,k)):T._d(i,T.st[-1]);T._r()
else:T.st.clear();raise KeyError
def __contains__(T,k):return 0<=T._f(T.r<<1,k)
def _f(T,s,k):
i = T.sub[s]
while~i and T.K[i]!=k:T._p(i);i=T.sub[i<<1|(T.K[i]<k)]
return i
def _t(T,s,k):
T.st.append(s)
while~(i:=T.sub[s])and T.K[i]!=k:T._p(i);T.st.append(s:=i<<1|(T.K[i]<k))
return i
def _i(T,s,k,n):
T.st.append(s)
while ~T.sub[s]:T._p(i:=T.sub[s]);T.st.append(s:=i<<1|(T.K[i]<k))
i,T.sub[s]=T.sub[s],n
def _d(T,i,s): raise NotImplemented
def _r(T):T.st.clear()
def _p(T,i): pass
@classmethod
def reserve(cls,sz):sz+=1;reserve(cls.K,sz);reserve(cls.sub,sz<<1);reserve(cls.st,sz.bit_length()<<1)
def _node_str(T, i): return f"{T.K[i]}"
def __str__(T):
def rec(i, pre="", is_right=False):
if i == -1: return ""
ret = "";T._p(i)
if ~(r:=T.sub[i<<1|1]):ret+=rec(r,pre+(" "if is_right else"│ "),True)
ret+=pre+("┌─ "if is_right else"└─ ")+T._node_str(i)+"\n"
if ~(l:=T.sub[i<<1]):ret+=rec(l,pre+(" "if not is_right else"│ "),False)
return ret
return rec(T.sub[T.r<<1]).rstrip()
class BSTUpdates(BST):
def _u(T,i): pass
def _r(T):
while T.st:T._u(T.st.pop()>>1)
class CartesianTree(BST):
K,P,sub,st=[-1],[42],[-1,-1],[]
def _nr(T):T.P.append(-1);return super()._nr()
def _nn(T,k,p=-1):T.P.append(p);return super()._nn(k)
def get(T,k):return T.P[BST.get(T,k)]
def pop(T,k):return T.P[BST.pop(T,k)]
def split(T,k):S=T._nt();T._sp(T.sub[T.r<<1],k,S.r<<1,T.r<<1);T._r();return S,T
def insert(T,k,p):T._i(T.r<<1,k,n:=T._nn(k,p));T._r();return n
def __getitem__(T,k):return T.get(k)
def _i(T,s,k,n):
T.st.append(s)
while~T.sub[s]and T.P[i:=T.sub[s]]<T.P[n]:T._p(i);T.st.append(s:=i<<1|(T.K[i]<k))
i,T.sub[s]=T.sub[s],n
if~i:T._sp(i,k,n<<1,n<<1|1)
def _sp(T,i,k,l,r):
T.st.append(l)
if 1<l^r:T.st.append(r)
while~i:
T._p(i)
if T.K[i]<k:T.sub[l]=i;i=T.sub[l:=i<<1|1];T.st.append(l)
else:T.sub[r]=i;i=T.sub[r:=i<<1];T.st.append(r)
T.sub[l]=T.sub[r]=-1
def _m(T,s,l,r):
T.st.append(s)
while~l and~r:
if T.P[l]<T.P[r]:T._p(l);T.sub[s]=l;l=T.sub[s:=l<<1|1]
else:T._p(r);T.sub[s]=r;r=T.sub[s:=r<<1]
T.st.append(s)
T.sub[s]=l if~l else r
def _d(T,i,s):T._p(i);T._m(s,T.sub[i<<1],T.sub[i<<1|1])
@classmethod
def reserve(cls,sz):super(CartesianTree,cls).reserve(sz);reserve(cls.P,sz+1)
class Treap(CartesianTree):
__slots__='e'
K,V,P,sub,st=[-1],[-1],[42],[-1,-1],[]
def __init__(T,e=-1):T.e=e;super().__init__()
def _nt(T):return T.__class__(T.e)
def _nr(T):T.V.append(T.e);return super()._nr()
def _nn(T,k,v):T.V.append(v);return super()._nn(k,(T.P[-1]*1103515245+12345)&0x7fffffff)
def insert(T,k,v):return super().insert(k,v)
def get(T,k):return T.V[BST.get(T,k)]
def pop(T,k):return T.V[BST.pop(T,k)]
def set(T,k,v):T._s(T.r<<1,k,v);T._r()
def __setitem__(T,k,v):T.set(k,v)
def _s(T,s,k,v):
if ~(i:=T._t(s,k)):T.V[i]=v;T.st.append(i<<1)
else:
n=T._nn(k,v)
while T.P[n]<T.P[i:=T.st[-1]>>1]:T._p(T.st.pop())
T._p(i)
i,T.sub[s]=T.sub[s:=i<<1|(i!=T.r and T.K[i]<k)],n
if~i:T._sp(i,k,n<<1,n<<1|1)
def _node_str(T, i): return f"{T.K[i]}:{T.V[i]}"
@classmethod
def reserve(cls,hint):super(Treap,cls).reserve(hint);reserve(cls.V,hint+1)
class TreapMonoid(Treap, BSTUpdates):
__slots__='op'
K,V,A,P,sub,st=[-1],[-1],[-1],[42],[-1,-1],[]
def __init__(T,op,e=-1):T.op=op;super().__init__(e)
def _nt(T):return T.__class__(T.op,T.e)
def _nr(T):T.A.append(T.e);return super()._nr()
def _nn(T,k,v):T.A.append(v);return super()._nn(k, v)
def prod(T,l,r):
# find common ancestor
a=T.sub[T.r<<1]
while~a and not l<=T.K[a]<r:T._p(a);a=T.sub[a<<1|(T.K[a]<l)]
if a<0:return T.e
# left subtreap
ac,i=T.V[a],T.sub[a<<1]
while~i:
T._p(i)
if not(b:=T.K[i]<l):
if~(j:=T.sub[i<<1|1]):ac=T.op(T.A[j],ac)
ac=T.op(T.V[i],ac)
i=T.sub[i<<1|b]
# right subtreap
i=T.sub[a<<1|1]
while~i:
T._p(i)
if b:=T.K[i]<r:
if~(j:=T.sub[i<<1]):ac=T.op(ac,T.A[j])
ac=T.op(ac,T.V[i])
i=T.sub[i<<1|b]
return ac
def all_prod(T):return T.A[T.r]
def __getitem__(T,k):
if isinstance(k,int):return T.get(k)
elif isinstance(k,slice):return T.prod(k.start,k.stop)
@classmethod
def reserve(cls,sz):super(TreapMonoid,cls).reserve(sz);reserve(cls.A,sz+1)
def _u(T,i):
T.A[i]=T.V[i]
if~(l:=T.sub[i<<1]):T.A[i]=T.op(T.A[l],T.A[i])
if~(r:=T.sub[i<<1|1]):T.A[i]=T.op(T.A[i],T.A[r])
def _v(T,i=None):
if i is None:
assert T.all_prod() == (ac := T._v(i) if ~(i := T.sub[T.r<<1]) else T.e)
return ac
T._p(i);ac = T.V[i]
if ~(l:=T.sub[i<<1]):
assert T.P[i] <= T.P[l]
assert T.K[l] <= T.K[i]
ac = T.op(T._v(l), ac)
if ~(r:=T.sub[i<<1|1]):
assert T.P[i] <= T.P[r]
assert T.K[i] <= T.K[r]
ac = T.op(ac, T._v(r))
assert T.A[i] == ac
return ac
def pack_enc(a: int, b: int, s: int): return a<<s|b
def pack_dec(ab: int, s: int, m: int): return ab>>s,ab&m
from typing import Iterable, Type, Union, overload
import typing
from collections import deque
from numbers import Number
from types import GenericAlias
from typing import Callable, Collection, Iterator, Union
import os
import sys
from io import BytesIO, IOBase
class FastIO(IOBase):
BUFSIZE = 8192
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
BUFSIZE = self.BUFSIZE
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
BUFSIZE = self.BUFSIZE
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
stdin: 'IOWrapper' = None
stdout: 'IOWrapper' = None
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
def write(self, s):
return self.buffer.write(s.encode("ascii"))
def read(self):
return self.buffer.read().decode("ascii")
def readline(self):
return self.buffer.readline().decode("ascii")
try:
sys.stdin = IOWrapper.stdin = IOWrapper(sys.stdin)
sys.stdout = IOWrapper.stdout = IOWrapper(sys.stdout)
except:
pass
from typing import TypeVar
_T = TypeVar('T')
_U = TypeVar('U')
class TokenStream(Iterator):
stream = IOWrapper.stdin
def __init__(self):
self.queue = deque()
def __next__(self):
if not self.queue: self.queue.extend(self._line())
return self.queue.popleft()
def wait(self):
if not self.queue: self.queue.extend(self._line())
while self.queue: yield
def _line(self):
return TokenStream.stream.readline().split()
def line(self):
if self.queue:
A = list(self.queue)
self.queue.clear()
return A
return self._line()
TokenStream.default = TokenStream()
class CharStream(TokenStream):
def _line(self):
return TokenStream.stream.readline().rstrip()
CharStream.default = CharStream()
ParseFn = Callable[[TokenStream],_T]
class Parser:
def __init__(self, spec: Union[type[_T],_T]):
self.parse = Parser.compile(spec)
def __call__(self, ts: TokenStream) -> _T:
return self.parse(ts)
@staticmethod
def compile_type(cls: type[_T], args = ()) -> _T:
if issubclass(cls, Parsable):
return cls.compile(*args)
elif issubclass(cls, (Number, str)):
def parse(ts: TokenStream): return cls(next(ts))
return parse
elif issubclass(cls, tuple):
return Parser.compile_tuple(cls, args)
elif issubclass(cls, Collection):
return Parser.compile_collection(cls, args)
elif callable(cls):
def parse(ts: TokenStream):
return cls(next(ts))
return parse
else:
raise NotImplementedError()
@staticmethod
def compile(spec: Union[type[_T],_T]=int) -> ParseFn[_T]:
if isinstance(spec, (type, GenericAlias)):
cls = typing.get_origin(spec) or spec
args = typing.get_args(spec) or tuple()
return Parser.compile_type(cls, args)
elif isinstance(offset := spec, Number):
cls = type(spec)
def parse(ts: TokenStream): return cls(next(ts)) + offset
return parse
elif isinstance(args := spec, tuple):
return Parser.compile_tuple(type(spec), args)
elif isinstance(args := spec, Collection):
return Parser.compile_collection(type(spec), args)
elif isinstance(fn := spec, Callable):
def parse(ts: TokenStream): return fn(next(ts))
return parse
else:
raise NotImplementedError()
@staticmethod
def compile_line(cls: _T, spec=int) -> ParseFn[_T]:
if spec is int:
fn = Parser.compile(spec)
def parse(ts: TokenStream): return cls([int(token) for token in ts.line()])
return parse
else:
fn = Parser.compile(spec)
def parse(ts: TokenStream): return cls([fn(ts) for _ in ts.wait()])
return parse
@staticmethod
def compile_repeat(cls: _T, spec, N) -> ParseFn[_T]:
fn = Parser.compile(spec)
def parse(ts: TokenStream): return cls([fn(ts) for _ in range(N)])
return parse
@staticmethod
def compile_children(cls: _T, specs) -> ParseFn[_T]:
fns = tuple((Parser.compile(spec) for spec in specs))
def parse(ts: TokenStream): return cls([fn(ts) for fn in fns])
return parse
@staticmethod
def compile_tuple(cls: type[_T], specs) -> ParseFn[_T]:
if isinstance(specs, (tuple,list)) and len(specs) == 2 and specs[1] is ...:
return Parser.compile_line(cls, specs[0])
else:
return Parser.compile_children(cls, specs)
@staticmethod
def compile_collection(cls, specs):
if not specs or len(specs) == 1 or isinstance(specs, set):
return Parser.compile_line(cls, *specs)
elif (isinstance(specs, (tuple,list)) and len(specs) == 2 and isinstance(specs[1], int)):
return Parser.compile_repeat(cls, specs[0], specs[1])
else:
raise NotImplementedError()
class Parsable:
@classmethod
def compile(cls):
def parser(ts: TokenStream): return cls(next(ts))
return parser
@overload
def read() -> list[int]: ...
@overload
def read(spec: Type[_T], char=False) -> _T: ...
@overload
def read(spec: _U, char=False) -> _U: ...
@overload
def read(*specs: Type[_T], char=False) -> tuple[_T, ...]: ...
@overload
def read(*specs: _U, char=False) -> tuple[_U, ...]: ...
def read(*specs: Union[Type[_T],_U], char=False):
if not char and not specs: return [int(s) for s in TokenStream.default.line()]
parser: _T = Parser.compile(specs)
ret = parser(CharStream.default if char else TokenStream.default)
return ret[0] if len(specs) == 1 else ret
def write(*args, **kwargs):
'''Prints the values to a stream, or to stdout_fast by default.'''
sep, file = kwargs.pop("sep", " "), kwargs.pop("file", IOWrapper.stdout)
at_start = True
for x in args:
if not at_start:
file.write(sep)
file.write(str(x))
at_start = False
file.write(kwargs.pop("end", "\n"))
if kwargs.pop("flush", False):
file.flush()
if __name__ == '__main__':
main()