Problem p02541 (python)

Fixed submission:
import sys

def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c for j in range(b)] for i in range(a)]
def list3d(a, b, c, d): return [[[d for k in range(c)] for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e for l in range(d)] for k in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
sys.setrecursionlimit(10**9)
INF = 10**19
MOD = 10**9 + 7
EPS = 10**-10

def factorize(num: int) -> dict:
    """ 素因数分解 """
    from math import sqrt
    from collections import Counter

    d = Counter()
    for i in range(2, int(sqrt(num))+1):
        while num % i == 0:
            num //= i
            d[i] += 1
        if num == 1:
            break
    if num != 1:
        d[num] += 1
    return d

def extgcd(a, b, x, y):
    """ 拡張ユークリッドの互除法(ax+by=gcd(a, b)の解を求める) """

    if b == 0:
        x = 1
        y = 0
        return (y, x)
    else:
        x, y = extgcd(b, a%b, y, x)
        y -= a // b * x
        return (y, x)

N = INT()

fact = list(factorize(N*2).items())
M = len(fact)

ans = N
for bit in range(1<<M):
    a = b = 1
    for i in range(M):
        if (bit>>i) & 1:
            a *= fact[i][0] ** fact[i][1]
        else:
            b *= fact[i][0] ** fact[i][1]
    y, x = extgcd(a, b, 0, 0)
    if x == 0 or y == 0:
        continue
    res = min(a*abs(x), b*abs(y))
    ans = min(ans, res)
print(ans)

Buggy submission (verdict: Runtime Error):
import sys

def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c for j in range(b)] for i in range(a)]
def list3d(a, b, c, d): return [[[d for k in range(c)] for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e for l in range(d)] for k in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
sys.setrecursionlimit(10**9)
INF = 10**19
MOD = 10**9 + 7
EPS = 10**-10

class BIT:
    """ Binary Indexed Tree """

    def __init__(self, n):
        self.n = n
        # 0-indexed
        n += 1
        nv = 1
        while nv < n:
            nv *= 2
        self.size = nv
        self.tree = [0] * nv

    def sum(self, i):
        """ [0, i]を合計する """
        s = 0
        i += 1
        while i > 0:
            s += self.tree[i-1]
            i -= i & -i
        return s

    def add(self, i, x):
        """ 値の追加：添字i, 値x """
        i += 1
        while i <= self.size:
            self.tree[i-1] += x
            i += i & -i

    def query(self, l, r):
        """ 区間和の取得 [l, r) """
        return self.sum(r-1) - self.sum(l-1)
    
    def get(self, i):
        """ 一点取得 """
        return self.query(i, i+1)

    def update(self, i, x):
        """ 値の更新：添字i, 値x """
        self.add(i, x - self.get(i))

    def print(self):
        for i in range(self.n):
            print(self.get(i), end=' ')
        print()

    def bisearch_fore(self, l, r, x):
        """ 区間[l, r]を左から右に向かってx番目の値がある位置 """
        l_sm = self.sum(l-1)
        ok = r + 1
        ng = l - 1
        while ng+1 < ok:
            mid = (ok+ng) // 2
            if self.sum(mid) - l_sm >= x:
                ok = mid
            else:
                ng = mid
        if ok != r + 1:
            return ok
        else:
            return INF

    def bisearch_back(self, l, r, x):
        """ 区間[l, r]を右から左に向かってx番目の値がある位置 """
        r_sm = self.sum(r)
        ok = l - 1
        ng = r + 1
        while ok+1 < ng:
            mid = (ok+ng) // 2
            if r_sm - self.sum(mid-1) >= x:
                ok = mid
            else:
                ng = mid
        if ok != l - 1:
            return ok
        else:
            return -INF

class UnionFind:
    """ Union-Find木 """

    def __init__(self, n):
        self.n = n
        self.par = [i for i in range(n)]
        self.rank = [0] * n
        self.size = [1] * n
        self.tree = [True] * n
        self.grpcnt = n

    def find(self, x):
        """ 根の検索(グループ番号の取得) """
        t = []
        while self.par[x] != x:
            t.append(x)
            x = self.par[x]
        for i in t:
            self.par[i] = x
        return self.par[x]

    def union(self, x, y):
        """ 併合 """
        x = self.find(x)
        y = self.find(y)

        if x == y:
            self.tree[x] = False
            return
        if not self.tree[x] or not self.tree[y]:
            self.tree[x] = self.tree[y] = False

        self.grpcnt -= 1
        if self.rank[x] < self.rank[y]:
            self.par[x] = y
            self.size[y] += self.size[x]
        else:
            self.par[y] = x
            self.size[x] += self.size[y]
            if self.rank[x] == self.rank[y]:
                self.rank[x] += 1

    def is_same(self, x, y):
        """ 同じ集合に属するか判定 """
        return self.find(x) == self.find(y)

    def get_size(self, x=None):
        if x is not None:
            """ あるノードの属する集合のノード数 """
            return self.size[self.find(x)]
        else:
            """ 集合の数 """
            return self.grpcnt
    
    def is_tree(self, x):
        """ 木かどうかの判定 """
        return self.tree[self.find(x)]

N = INT()
XY = []
XtoY = [0] * (N+1)
YtoI = [0] * (N+1)
for i in range(N):
    x, y = MAP()
    XY.append((x, y))
    XtoY[x] = (y, i)
    YtoI[y] = i

bit = BIT(N+1)
uf = UnionFind(N)
for i in range(1, N+1):
    bit.add(i, 1)
for x in range(1, N+1):
    y, i = XtoY[x]
    cury = y
    while 1:
        nxty = bit.bisearch_fore(cury+1, N, 1)
        if nxty == INF:
            break
        else:
            j = YtoI[nxty]
            if uf.is_same(i, j):
                break
            else:
                uf.union(i, j)
                cury = nxty
    bit.add(y, -1)

for i in range(N):
    ans = uf.get_size(i)
    print(ans)