#include using namespace std; using ll = long long; #ifdef MY_DEBUG #define dbg(...) debug_out(__VA_ARGS__) #define dbgn(var) debug_out(#var, "=", var) #else #define dbg(...) #define dbgn(...) #endif void debug_out(); template void debug_out(Head, Tail...); template bool chmax(T&, const T&); template bool chmin(T&, const T&); template T pwr(T, ll); template T squ(T x) { return x * x; } ll fact(ll); ll comb(ll, ll); ll ctoll(char); char lltoc(ll); bool flg(ll b, ll i) { return ((b) >> (i)) & 1LL; } // flg(0b010, 1LL) -> true const ll LINF = (ll)1e18 + 7; const double EPS = 1e-9; const int MAX_DUBUG_SIZE = 10; // 重み付きUnionFindライブラリで重みをxorにしたやつ struct weighted_union_find { vector par, rank, siz; // par: parent, rank: depth, siz: size of group vector diff_weight; ll group_num; // 連結成分の個数 weighted_union_find(ll n) : par(n, -1), rank(n, 0), siz(n, 1), diff_weight(n, false), group_num(n) {} ll root(ll x) { if (par[x] == -1) { return x; } else { ll root_id = root(par[x]); diff_weight[x] = diff_weight[x] ^ diff_weight[par[x]]; par[x] = root_id; // 経路圧縮、帰りがけに根に直接つなぐ return par[x]; } } bool is_same(ll x, ll y) { return root(x) == root(y); } bool weight(ll x) { root(x); return diff_weight[x]; } // unite by rank, x の根の下に y の根をつなぐ // w = weight(y) ^ weight(x) を満たすように // xとyの値が同じ <-> w = false bool unite(ll x, ll y, bool w) { // x と y の値が等しかったら y の根を x の根にポテンシャル0ではってyはそのまま、x と y の値が違うときは y の根を // x の根にポテンシャル1ではって y を反転させる w = w ^ weight(x); w = w ^ weight(y); ll rx = root(x), ry = root(y); if (rx == ry) { return false; } if (rank[rx] < rank[ry]) { swap(rx, ry); } if (rank[rx] == rank[ry]) { rank[rx]++; } par[ry] = rx; siz[rx] += siz[ry]; siz[ry] = 0; diff_weight[ry] = w; group_num--; return true; } ll size(ll x) { return siz[root(x)]; } bool diff(ll x, ll y) { return weight(y) ^ weight(x); } }; struct edge { ll to; ll w; // edge v; // v.to, v.w でメンバ変数を呼び出す edge(ll to, ll w) : to(to), w(w) {} // graph g(n); で n 頂点のグラフを宣言 // graph[from].push_back(edge(to, w)) の形で使う }; using graph = vector>; void solve([[maybe_unused]] int test) { ll n, m; cin >> n >> m; ll s, t, k; cin >> s >> t >> k; s--, t--; graph g(n); // 0-index, 無向グラフに直し忘れない。 vector a(m), b(m); for (ll i = 0; i < m; i++) { cin >> a[i] >> b[i]; a[i]--, b[i]--; g[a[i]].push_back(edge(b[i], 1)); g[b[i]].push_back(edge(a[i], 1)); } weighted_union_find wuf(n); for (ll i = 0; i < m; i++) { wuf.unite(a[i], b[i], true); } vector dist(n, LINF); priority_queue, vector>, greater>> q; dist[s] = 0; q.push({0, s}); while (q.size()) { auto [d, v] = q.top(); q.pop(); // 以下でdは使わないのでこの行はなくてもいいがあった方が速い if (d > dist[v]) continue; for (auto& x : g[v]) { auto [to, w] = x; if (chmin(dist[to], dist[v] + w)) { q.emplace(dist[to], to); } } } dbg(dist); // N = 1 のとき if (n == 1) { cout << "No" << '\n'; return; } // N = 2 のとき if (n == 2) { if (s == t) { if (g[s].size() == 0) { if (k % 2 == 0) { cout << "Unknown" << '\n'; } else { cout << "No" << '\n'; } } else { if (k % 2 == 0) { cout << "Yes" << '\n'; } else { cout << "No" << '\n'; } } } else { if (g[s].size() == 0) { if (k % 2 == 0) { cout << "No" << '\n'; } else { cout << "Unknown" << '\n'; } } else { if (k % 2 == 0) { cout << "No" << '\n'; } else { cout << "Yes" << '\n'; } } } return; } // 以下 n >= 3 // s = t のとき if (s == t and g[s].size() == 0) { if (k % 2 == 0) { cout << "Unknown" << '\n'; } else { cout << "No" << '\n'; } return; } // 非連結ならUnknown if (!wuf.is_same(s, t)) { cout << "Unknown" << '\n'; return; } // 色が違ってkが偶数 or 同色でkが奇数 ならNo if ((wuf.diff(s, t) and k % 2 == 0) or (!wuf.diff(s, t) and k % 2 == 1)) { cout << "No" << '\n'; return; } // sとtの最短経路がk以下ならYes if (dist[t] <= k) { cout << "Yes" << '\n'; return; } // それ以外はUnknown cout << "Unknown" << '\n'; } int main() { cin.tie(nullptr), ios::sync_with_stdio(false); cout << fixed << setprecision(12), cerr << fixed << setprecision(12); int testcase_size = 1; // cin >> testcase_size; for (int _t = 0; _t < testcase_size; _t++) { solve(_t); } } /* -----------------------------------MY_FUNCTIONS------------------------------------ */ template ostream& operator<<(ostream& os, const pair& pp) { return os << "{" << pp.first << "," << pp.second << "}"; } template ostream& operator<<(ostream& os, const vector& V) { if (V.empty()) return os << "[]"; os << "["; for (ll i = 0; i < (ll)V.size(); i++) { os << V[i] << (i == int(V.size() - 1) ? "]" : ","); } return os; } template ostream& operator<<(ostream& os, const vector>& VV) { if (VV.empty()) return os << "[[]]"; os << "[\n"; for (auto&& V : VV) { os << V << "\n"; } os << "]"; return os; } template ostream& operator<<(ostream& os, const vector>>& VVV) { if (VVV.empty()) return os << "[[[]]]"; os << "[" << "\n"; int cnt = 0; for (auto&& VV : VVV) { os << cnt++ << VV << "\n\n"; } os << "]"; return os; } template ostream& operator<<(ostream& os, const set& SS) { if (SS.empty()) return os << "[]"; os << "["; auto ii = SS.begin(); for (; ii != SS.end(); ii++) os << *ii << (ii == prev(SS.end()) ? "]" : ","); return os; } template ostream& operator<<(ostream& os, const map& MM) { if (MM.empty()) return os << "[{:}]"; os << "["; auto ii = MM.begin(); for (; ii != MM.end(); ii++) os << "{" << ii->first << ":" << ii->second << "}" << (ii == prev(MM.end()) ? "]" : ","); return os; } void debug_out() { cerr << endl; } void debug_out_vl(vector V) { const int MAX_SIZE = min((int)V.size(), MAX_DUBUG_SIZE); cerr << "\033[33m"; if (V.empty()) { cerr << "[]" << endl; return; } cerr << "["; for (int i = 0; i < MAX_SIZE; i++) { if (V[i] == LINF) cerr << "INF"; else cerr << V[i]; if (i == (int)V.size() - 1) cerr << "]\n"; else if (i == MAX_DUBUG_SIZE - 1) cerr << ",...\n"; else cerr << ","; } return; } void debug_out_vvl(vector> VV) { cerr << "\033[33m"; if (VV.empty()) { cerr << "[[]]" << endl; return; } cerr << "[\n"; int MAX_ROW = min((int)VV.size(), MAX_DUBUG_SIZE); for (int i = 0; i < MAX_ROW; i++) { const int MAX_COLUMN = min((int)VV[i].size(), MAX_DUBUG_SIZE); if (VV[i].empty()) { cerr << "[]" << endl; continue; } cerr << "["; for (int j = 0; j < MAX_COLUMN; j++) { if (VV[i][j] == LINF) cerr << "INF"; else cerr << VV[i][j]; if (j == (int)VV[i].size() - 1) cerr << "]\n"; else if (j == MAX_DUBUG_SIZE - 1) cerr << ",...\n"; else cerr << ","; } if (i != (int)VV.size() - 1 and i == MAX_DUBUG_SIZE - 1) { cerr << ":\n:\033[m\n"; return; } } cerr << "]\033[m\n"; return; } template void debug_out(Head H, Tail... T) { if constexpr (std::is_same_v>) { debug_out_vl(H); } else if constexpr (std::is_same_v>>) { debug_out_vvl(H); } else { cerr << "\033[33m" << H << "\033[m "; } debug_out(T...); } template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } return false; } template T pwr(T x, ll n) { T res = 1; for (int i = 0; i < n; i++) { res *= x; } return res; } ll fact(ll n) { ll res = 1; for (ll i = 1; i <= n; i++) res *= i; return res; } ll comb(ll n, ll r) { // comb(60, 30)までオーバーフローなし ll res = 1; for (int i = 1; i <= r; i++) { res *= n--; res /= i; } return res; } ll ctoll(char c) { if (c < '0' or '9' < c) { cerr << "\n\033[33m ctoll に '0'~'9' 以外の文字が入りました。\033[m\n" << endl; } return ll(c - '0'); } char lltoc(ll n) { if (n < 0 or 9 < n) { cerr << "\n\033[33m lltoc に 0 ~ 9 以外の数字が入りました。\033[m\n" << endl; } return char(n + '0'); }