#include using namespace std; #include typedef atcoder::modint998244353 mint; int main() { int n, m; cin >> n >> m; vector b(n); for (int i=0; i> x; b[i] = x; } vector u(m), v(m); vector ikeru(n, vector>(0)); for (int i=0; i> u[i] >> v[i]; u[i]--; v[i]--; ikeru[u[i]].push_back(pair(v[i], i)); ikeru[v[i]].push_back(pair(u[i], i)); } vector color(n); bool is_bipartite = true; vector odd_cycle_edge_list; vector odd_cycle_vertex_list; vector odd_cycle_vertex(n); vector tansaku(n); auto dfs = [&](auto self, int i) -> int { for (auto [j,e]: ikeru[i]) { if (tansaku[j]) { if (color[i] == color[j]) { is_bipartite = false; odd_cycle_edge_list.push_back(e); odd_cycle_vertex[i] = true; odd_cycle_vertex_list.push_back(i); return j; } }else{ tansaku[j] = true; color[j] = color[i] ^ 1; int v = self(self, j); if (v >= 0) { odd_cycle_edge_list.push_back(e); odd_cycle_vertex[i] = true; odd_cycle_vertex_list.push_back(i); if (v == i) return -1; return v; } } if (!is_bipartite) { return -1; } } return -1; }; tansaku[0] = true; dfs(dfs, 0); reverse(odd_cycle_edge_list.begin(), odd_cycle_edge_list.end()); reverse(odd_cycle_vertex_list.begin(), odd_cycle_vertex_list.end()); if (is_bipartite) { mint total = 0; for (int i=0; i>(0)); auto dfs2 = [&](auto self, int i) -> void { for(auto [j,e]: ikeru[i]) { if (tansaku[j]) continue; if (odd_cycle_vertex[j]) continue; tansaku[j] = 1; new_ikeru[i].push_back(pair(j, e)); new_ikeru[j].push_back(pair(i, e)); self(self, j); } }; fill(tansaku.begin(), tansaku.end(), false); if (is_bipartite) { tansaku[0] = true; dfs2(dfs2, 0); }else{ for (int i: odd_cycle_edge_list) { new_ikeru[u[i]].push_back(pair(v[i], i)); new_ikeru[v[i]].push_back(pair(u[i], i)); } for (int i: odd_cycle_vertex_list) { assert(!tansaku[i]); tansaku[i] = true; dfs2(dfs2, i); } } vector deg(n); for (int i=0; i mada; for (int i=0; i ans(m); while(!mada.empty()) { int i = mada.back(); mada.pop_back(); tansaku[i] = true; for (auto [j,e]: new_ikeru[i]) { if (tansaku[j]) continue; ans[e] = b[i]; b[i] -= ans[e]; b[j] -= ans[e]; deg[j] -= 1; if (deg[j] == 1) { mada.push_back(j); } } } if (!is_bipartite) { int k = (int)odd_cycle_edge_list.size(); mint total_weight = 0; for (int i: odd_cycle_vertex_list){ total_weight += b[i]; } total_weight *= mint(2).inv(); { int e = odd_cycle_edge_list[0]; ans[e] = total_weight; for (int i=2; i