結果
| 問題 | No.3567 Modulo Grid |
| コンテスト | |
| ユーザー |
 lif4635
|
| 提出日時 | 2026-06-05 22:08:22 |
| 言語 | PyPy3 (7.3.17) |
| 結果 |
AC
|
| 実行時間 | 233 ms / 2,000 ms |
| コード長 | 9,603 bytes |
| 記録 | |
| コンパイル時間 | 560 ms |
| コンパイル使用メモリ | 85,504 KB |
| 実行使用メモリ | 124,416 KB |
| 最終ジャッジ日時 | 2026-06-05 22:08:34 |
| 合計ジャッジ時間 | 6,003 ms |
|
ジャッジサーバーID （参考情報） |
judge1_1 / judge3_0 |
| 純コード判定待ち |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 25 |
ソースコード
# input
import sys
input = sys.stdin.readline
II = lambda : int(input())
MI = lambda : map(int, input().split())
LI = lambda : [int(a) for a in input().split()]
SI = lambda : input().rstrip()
LLI = lambda n : [[int(a) for a in input().split()] for _ in range(n)]
LSI = lambda n : [input().rstrip() for _ in range(n)]
MI_1 = lambda : map(lambda x:int(x)-1, input().split())
LI_1 = lambda : [int(a)-1 for a in input().split()]
mod = 998244353
inf = 1001001001001001001
ordalp = lambda s : ord(s)-65 if s.isupper() else ord(s)-97
ordallalp = lambda s : ord(s)-39 if s.isupper() else ord(s)-97
yes = lambda : print("Yes")
no = lambda : print("No")
yn = lambda flag : print("Yes" if flag else "No")
prinf = lambda ans : print(ans if ans < 1000001001001001001 else -1)
alplow = "abcdefghijklmnopqrstuvwxyz"
alpup = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
alpall = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"
URDL = {'U':(-1,0), 'R':(0,1), 'D':(1,0), 'L':(0,-1)}
DIR_4 = [[-1,0],[0,1],[1,0],[0,-1]]
DIR_8 = [[-1,0],[-1,1],[0,1],[1,1],[1,0],[1,-1],[0,-1],[-1,-1]]
DIR_BISHOP = [[-1,1],[1,1],[1,-1],[-1,-1]]
prime60 = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59]
sys.set_int_max_str_digits(0)
# sys.setrecursionlimit(10**6)
# import pypyjit
# pypyjit.set_param('max_unroll_recursion=-1')
from collections import defaultdict,deque
from heapq import heappop,heappush
from bisect import bisect_left,bisect_right
DD = defaultdict
BSL = bisect_left
BSR = bisect_right
def inv_gcd(a, b):
a = a % b
if a == 0:
return (b, 0)
s = b
t = a
m0 = 0
m1 = 1
while t:
u = s // t
s -= t * u
m0 -= m1 * u
s, t = t, s
m0, m1 = m1, m0
if m0 < 0:
m0 += b // s
return (s, m0)
def inv_mod(x, m):
assert 1 <= m
z = inv_gcd(x, m)
assert z[0] == 1
return z[1]
def crt(r, m):
assert len(r) == len(m)
n = len(r)
r0 = 0
m0 = 1
for i in range(n):
assert 1 <= m[i]
r1 = r[i] % m[i]
m1 = m[i]
if m0 < m1:
r0, r1 = r1, r0
m0, m1 = m1, m0
if m0 % m1 == 0:
if r0 % m1 != r1:
return (0, 0)
continue
g, im = inv_gcd(m0, m1)
u1 = m1 // g
if (r1 - r0) % g:
return (0, 0)
x = (r1 - r0) // g % u1 * im % u1
r0 += x * m0
m0 *= u1
if r0 < 0:
r0 += m0
return (r0, m0)
def floor_sum(n, m, a, b):
ans = 0
while True:
if a < 0 or a >= m:
k = a // m
a = a % m
if a < 0:
a += m
k -= 1
ans += k * n * (n - 1) // 2
if b < 0 or b >= m:
k = b // m
b = b % m
if b < 0:
b += m
k -= 1
ans += k * n
y_max = (a * n + b) // m
if y_max == 0:
break
x_max = y_max * m - b
ans += (n - (x_max + a - 1) // a) * y_max
n, m, a, b = y_max, a, m, (a - x_max % a) % a
return ans
from math import isqrt
from random import randint
def gcd(x, y):
""" x < y """
while y:
x, y = y, x%y
return x
def is_prime(num):
""" 1 <= x < 1<<64 """
if num < 4: return num > 1
if not num&1: return False
d, s = num-1, 0
while not d&1:
d >>= 1
s += 1
tests = (2,7,61) if num < 4759123141 else (2,325,9375,28178,450775,9780504,1795265022)
for test in tests:
if test >= num: return True
t = pow(test, d, num)
if 1 < t < num-1:
for _ in range(s-1):
t = t*t%num
if t == num-1: break
else:
return False
return True
def find_prime(n):
b = n.bit_length() - 1
b = (b >> 2) << 2
m = (1 << (b >> 3)) << 1
while True:
c = randint(1, n - 1)
y = 0
g = q = r = 1
while g == 1:
x = y
for _ in range(r):
y = (y * y + c) % n
k = 0
while k < r and g == 1:
ys = y
for _ in range(min(m, r - k)):
y = (y * y + c) % n
q = q * abs(x - y) % n
g = gcd(q, n)
k += m
r <<= 1
if g == n:
g = 1
y = ys
while g == 1:
y = (y * y + c) % n
g = gcd(abs(x - y), n)
if g == n:
continue
if is_prime(g):
return g
elif is_prime(n // g):
return n // g
else:
n = g
def _primefactor(n):
result = []
for p in range(2, 500):
if p * p > n:
break
c = 0
while n%p == 0:
n //= p
c += 1
if c:
result.append(p)
while n > 1 and not is_prime(n):
p = find_prime(n)
while n % p == 0:
n //= p
result.append(p)
if n > 1: result.append(n)
return result
def primefact(n, deduplicate = True):
if deduplicate == False:
return _primefactor(n)
result = dict()
for p in range(2, 500):
if p * p > n:
break
c = 0
while n%p == 0:
n //= p
c += 1
if c:
result[p] = c
while n > 1 and not is_prime(n):
p = find_prime(n)
c = 0
while n % p == 0:
n //= p
c += 1
result[p] = c
if n > 1: result[n] = 1
return result
def divisors_naive(n):
divs_small, divs_big = [], []
i = 1
while i*i <= n:
if n % i == 0:
divs_small.append(i)
if i != n//i:
divs_big.append(n//i)
i += 1
return divs_small + divs_big[::-1]
def divisors(n):
if n == 1: return [1]
if n <= 100_000_000: # 10 ** 8
return divisors_naive(n)
pf = primefact(n)
ps = list(pf.keys())
es = list(pf.values())
us = [p ** e for p,e in zip(ps, es)]
l = len(es)
nes = [0] * (l + 1)
r = 1
res = [1]
while True:
nes[0] += 1
for i in range(l):
if nes[i] > es[i]:
if i+1 == l:
res.sort()
return res
nes[i] = 0
nes[i+1] += 1
r //= us[i]
else:
r *= ps[i]
break
res.append(r)
def totient(n):
"""
totient(n) = #{ m | (m,n) = 1, 1 <= m <= n }
"""
pf = _primefactor(n)
for p in pf:
n //= p
n *= p - 1
return n
def mobius(n):
pf = primefact(n)
r = 1
for p,e in pf.items():
if e >= 2: return 0
r *= -1
return r
def primitive_root(p):
""" p : prime """
if p == 2: return 1
r = p - 1
tests = []
for q in range(2, 500):
if q * q > r:
break
if r % q == 0:
while r % q == 0:
r //= q
tests.append((p - 1) // q)
while r > 1 and not is_prime(r):
q = find_prime(r)
while r % q == 0:
r //= q
tests.append((p - 1) // q)
if r > 1: tests.append((p - 1) // r)
res = 2
while True:
for test in tests:
if pow(res, test, p) == 1:
break
else:
return res
res = randint(3, p - 2)
def check(h, w, a):
m = h * w
for i in range(h):
for j in range(w - 1):
f = 0
for x in range(1, m):
if a[i][j] * x % m == a[i][j+1]:
f = 1
if a[i][j] == a[i][j+1] * x % m:
f = 1
if f == 0:
return False
for i in range(h - 1):
for j in range(w):
f = 0
for x in range(1, m):
if a[i][j] * x % m == a[i+1][j]:
f = 1
if a[i][j] == a[i+1][j] * x % m:
f = 1
if f == 0:
return False
return True
from math import gcd
"""
gcd が割り切れば ok
素数を一つだけ変える
"""
def calc(ps):
now = [tuple()]
for x in ps:
# x = p ** e
nxt = []
for y in range(x):
c = now if y & 1 else reversed(now)
for v in c:
nxt.append(v + (y,))
now = nxt
return now
def solve(h, w):
m = h * w
pf = primefact(m)
# これのべき
ph = []
pw = []
pm = []
for p, e in pf.items():
eh = 0
h_ = h
while h_ % p == 0:
h_ //= p
eh += 1
ew = e - eh
ph.append(p ** eh)
pw.append(p ** ew)
pm.append(p ** e)
ans = [[0] * w for i in range(h)]
# 列ごとに
r = calc(ph[:])
c = calc(pw[:])
# print(r)
# print(c)
for i in range(h):
for j in range(w):
p = []
q = []
# 素数ごとにつくっておいて cht でもどす
for k in range(len(pf)):
p.append((r[i][k] + ph[k] * c[j][k]) % pm[k])
q.append(pm[k])
ans[i][j] = crt(p, q)[0]
if ans[i][j] == 0:
ans[i][j] = m
return ans
h, w = MI()
ans = solve(h, w)
for e in ans:
print(*e)
# for h in range(2, 5):
# for w in range(2, 5):
# ans = solve(h, w)
# check(h, w, ans)