#include #define N_MAX 150 #define M_MAX 12000 typedef struct Edge { struct Edge *next; int v; unsigned int label; } edge; void chmin(int* a, int b) { if (*a > b) *a = b; } int lex_smaller(int a[], int b[]) { int i; for (i = 0; i <= a[0]; i++) { if (a[i] < b[i]) return 1; else if (a[i] > b[i]) return -1; } return 0; } void chlexmin(int a[], int b[]) { int i; if (lex_smaller(a, b) < 0) for (i = 0; i <= b[0]; i++) a[i] = b[i]; } void print_ans(int N, int ans[]) { int i; if (ans[0] > N) { printf("-1\n"); return; } else printf("%d\n", ans[0]); for (i = 1; i <= ans[0]; i++) printf("%d ", ans[i]); printf("%d\n", ans[1]); } #define MT_N 624 #define MT_M 397 #define MT_MATRIX_A 0x9908b0dfUL #define MT_UPPER_MASK 0x80000000UL #define MT_LOWER_MASK 0x7fffffffUL static unsigned int mt[MT_N]; static int mti = MT_N + 1; void init_genrand(unsigned int s) { mt[0] = s & 0xffffffffUL; for (mti = 1; mti < MT_N; mti++) { mt[mti] = (1812433253UL * (mt[mti-1] ^ (mt[mti-1] >> 30)) + mti); mt[mti] &= 0xffffffffUL; } } unsigned int genrand() { unsigned int y; static unsigned int mag01[2] = {0x0UL, MT_MATRIX_A}; if (mti >= MT_N) { int kk; if (mti == MT_N + 1) init_genrand(5489UL); for (kk = 0; kk < MT_N - MT_M; kk++) { y = (mt[kk] & MT_UPPER_MASK) | (mt[kk+1] & MT_LOWER_MASK); mt[kk] = mt[kk+MT_M] ^ (y >> 1) ^ mag01[y&0x1UL]; } for (; kk < MT_N - 1; kk++) { y = (mt[kk] & MT_UPPER_MASK) | (mt[kk+1] & MT_LOWER_MASK); mt[kk] = mt[kk+(MT_M-MT_N)] ^ (y >> 1) ^ mag01[y&0x1UL]; } y = (mt[MT_N-1] & MT_UPPER_MASK) | (mt[0] & MT_LOWER_MASK); mt[MT_N-1] = mt[MT_M-1] ^ (y >> 1) ^ mag01[y&0x1UL]; mti = 0; } y = mt[mti++]; y ^= (y >> 11); y ^= (y << 7) & 0x9d2c5680UL; y ^= (y << 15) & 0xefc60000UL; y ^= (y >> 18); return y; } #define POWX 4 // 3 -> 2^8, 4 -> 2^16, 5 -> 2^32 const unsigned int powd[6] = {2, 4, 16, 256, 65536}, powe[6] = {1, 2, 4, 8, 16, 32}; // Multiplication on a finite field of size 2^32 with XOR addition unsigned int nim_product(unsigned int A, unsigned int B) { if (A > B) return nim_product(B, A); else if (A <= 1) return A * B; static unsigned int memo[256][256] = {}; if (B < 256 && memo[A][B] != 0) return memo[A][B]; int i; for (i = 0; i < POWX; i++) { if (B == powd[i]) { if (A == powd[i]) return (B >> 1) * 3; else return A * B; } } unsigned int a[2], b[2], ans[2][2]; for (i = POWX - 1; i >= 0; i--) if (B > powd[i]) break; a[1] = A & (powd[i] - 1); a[0] = (A ^ a[1]) >> powe[i]; b[1] = B & (powd[i] - 1); b[0] = (B ^ b[1]) >> powe[i]; ans[0][0] = nim_product(a[0], b[0]); ans[0][1] = nim_product(a[0], b[1]); ans[1][0] = nim_product(a[1], b[0]); ans[1][1] = nim_product(a[1], b[1]); if (B < 256) { memo[A][B] = (ans[0][0] ^ ans[0][1] ^ ans[1][0]) * powd[i] ^ nim_product(ans[0][0], powd[i] >> 1) ^ ans[1][1]; return memo[A][B]; } else return (ans[0][0] ^ ans[0][1] ^ ans[1][0]) * powd[i] ^ nim_product(ans[0][0], powd[i] >> 1) ^ ans[1][1]; } int solve4_lexmin_sub(int N, int X, int Y, int Z, edge* adj[], edge* d_adj[][N_MAX + 1], int s, int flag[]) { static int i, k, kk, l, n, u, w, x, y, z; static unsigned int dp[N_MAX + 1][4][N_MAX + 1], tmp; static edge *p; kk = ((flag[Y] != 0)? 1: 0) | ((flag[Z] != 0)? 2: 0); for (u = 1, n = 0; u <= N; u++) if (flag[u] == 0) n++; for (l = 0; l <= N; l++) for (k = 0; k < 4; k++) for (u = 1; u <= N; u++) dp[l][k][u] = 0; for (p = adj[X]; p != NULL; p = p->next) if (flag[p->v] == 0) dp[1][kk][p->v] = p->label; for (l = 1; l <= n; l++) { for (p = adj[s]; p != NULL; p = p->next) if (flag[p->v] == 0 && dp[l][3][p->v] != 0) break; if (p != NULL) break; if (flag[Y] == 0) { for (p = d_adj[1][s]; p != NULL; p = p->next) if (flag[p->v] == 0 && dp[l-1][2][p->v] != 0) break; if (p != NULL) break; } if (flag[Z] == 0) { for (p = d_adj[2][s]; p != NULL; p = p->next) if (flag[p->v] == 0 && dp[l-1][1][p->v] != 0) break; if (p != NULL) break; } if (l == n) return -1; for (k = 0; k < 4; k++) { if ((k & kk) != kk) continue; for (y = 1; y <= N; y++) { if (flag[y] != 0 || y == X || y == Y || y == Z) continue; tmp = dp[l][k][y]; for (p = adj[y]; p != NULL; p = p->next) { z = p->v; dp[l+1][k][z] ^= nim_product(tmp, p->label); } if (l == n - 1) continue; if ((k & 1) == 0) { for (p = d_adj[1][y]; p != NULL; p = p->next) { z = p->v; dp[l+2][k|1][z] ^= nim_product(tmp, p->label); } } if ((k & 2) == 0) { for (p = d_adj[2][y]; p != NULL; p = p->next) { z = p->v; dp[l+2][k|2][z] ^= nim_product(tmp, p->label); } } } } } int ans = N + 1; for (p = adj[s]; p != NULL; p = p->next) if (flag[p->v] == 0 && dp[l][3][p->v] != 0) chmin(&ans, p->v); if (ans < Y) return ans; else if (flag[Y] == 0) for (p = d_adj[1][s]; p != NULL; p = p->next) if (flag[p->v] == 0 && dp[l-1][2][p->v] != 0) ans = Y; if (ans < Z) return ans; else if (flag[Z] == 0) for (p = d_adj[2][s]; p != NULL; p = p->next) if (flag[p->v] == 0 && dp[l-1][1][p->v] != 0) ans = Z; return ans; } // Solution example (O(N^4) time with all speeding-up) for finding the lexmin solution int solve4_lexmin(int N, int M, int X, int Y, int Z, int A[], int B[], int ans[]) { static int i, u, w, adj_mat[N_MAX + 1][N_MAX + 1]; static edge *adj[N_MAX + 1], e[M_MAX * 2], *p, *pp; for (u = 1; u <= N; u++) for (w = u + 1; w <= N; w++) adj_mat[u][w] = 0; for (i = 1; i <= M; i++) { u = A[i]; w = B[i]; adj_mat[u][w] = 1; } for (u = 1; u <= N; u++) adj[u] = NULL; for (u = 1, i = 0; u <= N; u++) { for (w = u + 1; w <= N; w++) { if (adj_mat[u][w] != 0) continue; e[i].v = w; e[i].label = genrand() % (powd[POWX] - 1) + 1; e[i].next = adj[u]; adj[u] = &(e[i++]); e[i].v = u; e[i].label = (u == X || w == X)? genrand() % (powd[POWX] - 1) + 1: e[i-1].label; e[i].next = adj[w]; adj[w] = &(e[i++]); } } static edge *d_adj[3][N_MAX + 1], f[N_MAX * N_MAX * 2]; for (u = 1; u <= N; u++) { d_adj[1][u] = NULL; d_adj[2][u] = NULL; } for (p = adj[Y], i = 0; p != NULL; p = p->next) { u = p->v; for (pp = p->next; pp != NULL; pp = pp->next) { w = pp->v; f[i].v = w; f[i].label = nim_product(p->label, pp->label); f[i].next = d_adj[1][u]; d_adj[1][u] = &(f[i++]); f[i].v = u; f[i].label = f[i-1].label; f[i].next = d_adj[1][w]; d_adj[1][w] = &(f[i++]); } } for (p = adj[Z]; p != NULL; p = p->next) { u = p->v; for (pp = p->next; pp != NULL; pp = pp->next) { w = pp->v; f[i].v = w; f[i].label = nim_product(p->label, pp->label); f[i].next = d_adj[2][u]; d_adj[2][u] = &(f[i++]); f[i].v = u; f[i].label = f[i-1].label; f[i].next = d_adj[2][w]; d_adj[2][w] = &(f[i++]); } } static int flag[N_MAX + 1]; for (u = 1; u <= N; u++) flag[u] = 0; ans[1] = X; ans[2] = solve4_lexmin_sub(N, X, Y, Z, adj, d_adj, X, flag); if (ans[2] < 0) { ans[0] = N + 1; for (i = 1; i <= N + 1; i++) ans[i] = 0; return -1; } else ans[0] = 2; flag[ans[1]] = 1; flag[ans[2]] = 1; while (1) { u = ans[ans[0]]; if (flag[Y] != 0 && flag[Z] != 0) { for (p = adj[u]; p != NULL; p = p->next) if (p->v == X) break; if (p != NULL) break; } w = solve4_lexmin_sub(N, X, Y, Z, adj, d_adj, u, flag); flag[w] = 1; ans[++ans[0]] = w; } return ans[0]; } int main() { int i, N, M, X, Y, Z, A[M_MAX + 1], B[M_MAX + 1], ans[2][N_MAX + 2]; scanf("%d %d", &N, &M); scanf("%d %d %d", &X, &Y, &Z); for (i = 1; i <= M; i++) scanf("%d %d", &(A[i]), &(B[i])); solve4_lexmin(N, M, X, Y, Z, A, B, ans[0]); solve4_lexmin(N, M, X, Y, Z, A, B, ans[1]); chlexmin(ans[0], ans[1]); // solve4_lexmin(N, M, X, Y, Z, A, B, ans[1]); // chlexmin(ans[0], ans[1]); print_ans(N, ans[0]); fflush(stdout); return 0; }