This documentation is automatically generated by online-judge-tools/verification-helper
import cp_library.__header__
import cp_library.math.__header__
import cp_library.math.conv.__header__
from cp_library.math.conv.fwht_fn import fwht
import cp_library.math.conv.mod.__header__
def fwht_inv(A: list[int], N: int, mod: int) -> list[int]:
fwht(A, N)
inv = pow(1 << N, -1, mod)
for i, a in enumerate(A): A[i] = a%mod * inv%mod
return A
'''
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
https://kobejean.github.io/cp-library
'''
'''
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
x₀ ────────●─●────────●───●────────●───────●────────► X₀
╳ ╲ ╱ ╲ ╱
x₄ ────────●─●────────●─╳─●────────●─╲───╱─●────────► X₁
╳ ╳ ╲ ╲ ╱ ╱
x₂ ────────●─●────────●─╳─●────────●─╲─╳─╱─●────────► X₂
╳ ╱ ╲ ╲ ╳ ╳ ╱
x₆ ────────●─●────────●───●────────●─╳─╳─╳─●────────► X₃
╳ ╳ ╳ ╳
x₁ ────────●─●────────●───●────────●─╳─╳─╳─●────────► X₄
╳ ╲ ╱ ╱ ╳ ╳ ╲
x₅ ────────●─●────────●─╳─●────────●─╱─╳─╲─●────────► X₅
╳ ╳ ╱ ╱ ╲ ╲
x₃ ────────●─●────────●─╳─●────────●─╱───╲─●────────► X₆
╳ ╱ ╲ ╱ ╲
x₇ ────────●─●────────●───●────────●───────●────────► X₇
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
Math - Convolution
'''
def fwht(A: list, N: int):
Z = len(A)
for i in range(N):
m = b = 1<<i
while m < Z:
a0, a1 = A[m^b], A[m]
A[m^b], A[m] = a0+a1, a0-a1
m = m+1|b
return A
def fwht_inv(A: list[int], N: int, mod: int) -> list[int]:
fwht(A, N)
inv = pow(1 << N, -1, mod)
for i, a in enumerate(A): A[i] = a%mod * inv%mod
return A