from collections import deque from dataclasses import dataclass class mf_graph: @dataclass class edge: from_: int to: int cap: int flow: int # def __init__(self, from_, to, cap, flow): # self.from_ = from_ # self.to = to # self.cap = cap # self.flow = flow @dataclass class _edge: to: int rev: int cap: int # def __init__(self, to, rev, cap): # self.to = to # self.rev = rev # self.cap = cap def __init__(self, n): self.n = n self.G = [[] for _ in range(n)] self.pos = [] def add_edge(self, from_, to, cap): m = len(self.pos) self.pos.append((from_, len(self.G[from_]))) from_id = len(self.G[from_]) to_id = len(self.G[to]) if from_ == to: to_id += 1 self.G[from_].append(mf_graph._edge(to, to_id, cap)) self.G[to].append(mf_graph._edge(from_, from_id, 0)) return m def get_edge(self, i): _e = self.G[self.pos[i][0]][self.pos[i][1]] _re = self.G[_e.to][_e.rev] return mf_graph.edge(self.pos[i][0], _e.to, _e.cap + _re.cap, _re.cap) def edges(self): m = len(self.pos) result = [] for i in range(m): result.append(self.get_edge(i)) return result def change_edge(self, i, new_cap, new_flow): _e = self.G[self.pos[i][0]][self.pos[i][1]] self.G[_e.to][_e.rev].cap = new_flow self.G[self.pos[i][0]][self.pos[i][1]].cap = new_cap - new_flow def flow(self, s, t, flow_limit=1 << 60): level = [] iter = [] que = deque() def bfs(): nonlocal level level = [-1] * self.n level[s] = 0 que.clear() que.append(s) while que: v = que.popleft() for e in self.G[v]: if e.cap == 0 or level[e.to] >= 0: continue level[e.to] = level[v] + 1 if e.to == t: return que.append(e.to) def dfs(v, up): if v == s: return up nonlocal level, iter res = 0 level_v = level[v] while iter[v] < len(self.G[v]): i = iter[v] iter[v] += 1 e = self.G[v][i] if level_v <= level[e.to] or self.G[e.to][e.rev].cap == 0: continue d = dfs(e.to, min(up - res, self.G[e.to][e.rev].cap)) if d <= 0: continue self.G[v][i].cap += d self.G[e.to][e.rev].cap -= d res += d if res == up: return res level[v] = self.n return res flow = 0 while flow < flow_limit: bfs() if level[t] == -1: break iter = [0] * self.n f = dfs(t, flow_limit - flow) if f == 0: break flow += f return flow def min_cut(self, s): visited = [False] * self.n que = deque() que.append(s) while que: p = que.popleft() visited[p] = True for e in self.G[p]: if e.cap and not visited[e.to]: visited[e.to] = True que.append(e.to) return visited n, m = map(int, input().split()) A = [list(map(int, input().split())) for _ in range(n)] for i in range(n): tot1 = 0 tot2 = 0 for j in range(n): tot1 += A[i][j] tot2 += A[j][i] if tot1 != m or tot2 != m: print(-1) exit() for _ in range(m): G = mf_graph(2 * n + 2) s = 2 * n t = 2 * n + 1 for i in range(n): G.add_edge(s, i, 1) G.add_edge(n + i, t, 1) for j in range(n): if A[i][j]: G.add_edge(i, n + j, 1) G.flow(s, t) P = [-1] * n for e in G.edges(): if e.from_ != s and e.to != t and e.flow == 1: P[e.from_] = e.to - n + 1 A[e.from_][e.to - n] -= 1 print(*P)