For problem statement at 0-999/500-599/510-519/512/problemD.txt this is a correct solution, but verifier at 0-999/500-599/510-519/512/verifierD.go ends with All 204 tests passed can you fix the verifier? package main

import (
	"bufio"
	"fmt"
	"os"
)

const MOD = 1000000009

func add(a, b int) int {
	return (a + b) % MOD
}

func sub(a, b int) int {
	return (a - b%MOD + MOD) % MOD
}

func mul(a, b int) int {
	return int((int64(a) * int64(b)) % MOD)
}

func power(base, exp int) int {
	res := 1
	base %= MOD
	for exp > 0 {
		if exp%2 == 1 {
			res = mul(res, base)
		}
		base = mul(base, base)
		exp /= 2
	}
	return res
}

func inv(n int) int {
	return power(n, MOD-2)
}

func poly_add(a, b []int) []int {
	sz := len(a)
	if len(b) > sz {
		sz = len(b)
	}
	res := make([]int, sz)
	for i := 0; i < sz; i++ {
		if i < len(a) {
			res[i] = add(res[i], a[i])
		}
		if i < len(b) {
			res[i] = add(res[i], b[i])
		}
	}
	return res
}

func poly_sub(a, b []int) []int {
	sz := len(a)
	if len(b) > sz {
		sz = len(b)
	}
	res := make([]int, sz)
	for i := 0; i < sz; i++ {
		if i < len(a) {
			res[i] = add(res[i], a[i])
		}
		if i < len(b) {
			res[i] = sub(res[i], b[i])
		}
	}
	return res
}

func poly_mul(a, b []int) []int {
	if len(a) == 0 || len(b) == 0 {
		return []int{}
	}
	res := make([]int, len(a)+len(b)-1)
	for i := 0; i < len(a); i++ {
		for j := 0; j < len(b); j++ {
			res[i+j] = add(res[i+j], mul(a[i], b[j]))
		}
	}
	return res
}

var inv_arr []int

func solve_tree(u, p int, adj [][]int, in_K []bool) (int, int, []int) {
	S_u := 1
	W_full := 1
	DP_u := []int{1}

	for _, v := range adj[u] {
		if v == p || in_K[v] {
			continue
		}

		S_v, W_v, DP_v := solve_tree(v, u, adj, in_K)
		S_u += S_v
		W_full = mul(W_full, W_v)

		poly_v := make([]int, len(DP_v))
		copy(poly_v, DP_v)
		for len(poly_v) <= S_v {
			poly_v = append(poly_v, 0)
		}
		poly_v[S_v] = add(poly_v[S_v], W_v)

		DP_u = poly_mul(DP_u, poly_v)
	}
	W_full = mul(W_full, inv_arr[S_u])
	return S_u, W_full, DP_u
}

func main() {
	reader := bufio.NewReader(os.Stdin)
	var n, m int
	if _, err := fmt.Fscan(reader, &n, &m); err != nil {
		return
	}

	adj := make([][]int, n+1)
	for i := 0; i < m; i++ {
		var u, v int
		fmt.Fscan(reader, &u, &v)
		adj[u] = append(adj[u], v)
		adj[v] = append(adj[v], u)
	}

	inv_arr = make([]int, n+1)
	for i := 1; i <= n; i++ {
		inv_arr[i] = inv(i)
	}

	fact := make([]int, n+1)
	fact[0] = 1
	for i := 1; i <= n; i++ {
		fact[i] = mul(fact[i-1], i)
	}

	deg := make([]int, n+1)
	for u := 1; u <= n; u++ {
		deg[u] = len(adj[u])
	}

	q := []int{}
	in_K := make([]bool, n+1)
	for u := 1; u <= n; u++ {
		in_K[u] = true
		if deg[u] <= 1 {
			q = append(q, u)
			in_K[u] = false
		}
	}

	for len(q) > 0 {
		u := q[0]
		q = q[1:]
		for _, v := range adj[u] {
			if in_K[v] {
				deg[v]--
				if deg[v] <= 1 {
					in_K[v] = false
					q = append(q, v)
				}
			}
		}
	}

	visited := make([]bool, n+1)
	components := [][]int{}
	for u := 1; u <= n; u++ {
		if !visited[u] {
			comp := []int{}
			q_bfs := []int{u}
			visited[u] = true
			for len(q_bfs) > 0 {
				v := q_bfs[0]
				q_bfs = q_bfs[1:]
				comp = append(comp, v)
				for _, w := range adj[v] {
					if !visited[w] {
						visited[w] = true
						q_bfs = append(q_bfs, w)
					}
				}
			}
			components = append(components, comp)
		}
	}

	F := []int{1}

	for _, comp := range components {
		has_K := false
		for _, u := range comp {
			if in_K[u] {
				has_K = true
				break
			}
		}

		if has_K {
			P_C := []int{1}
			for _, u := range comp {
				if !in_K[u] {
					is_adj := false
					for _, v := range adj[u] {
						if in_K[v] {
							is_adj = true
							break
						}
					}
					if is_adj {
						S_u, W_u, DP_u := solve_tree(u, -1, adj, in_K)
						poly_u := make([]int, len(DP_u))
						copy(poly_u, DP_u)
						for len(poly_u) <= S_u {
							poly_u = append(poly_u, 0)
						}
						poly_u[S_u] = add(poly_u[S_u], W_u)
						P_C = poly_mul(P_C, poly_u)
					}
				}
			}
			F = poly_mul(F, P_C)
		} else {
			P_non_empty := make([]int, 0)
			for _, v := range comp {
				_, _, DP_v := solve_tree(v, -1, adj, in_K)
				P_non_empty = poly_add(P_non_empty, DP_v)
			}

			for i := 0; i < len(comp); i++ {
				u := comp[i]
				for _, w := range adj[u] {
					if u < w {
						_, _, DP_u := solve_tree(u, w, adj, in_K)
						_, _, DP_w := solve_tree(w, u, adj, in_K)
						P_e := poly_mul(DP_u, DP_w)
						P_non_empty = poly_sub(P_non_empty, P_e)
					}
				}
			}

			W_empty := 0
			for _, v := range comp {
				_, W_v, _ := solve_tree(v, -1, adj, in_K)
				W_empty = add(W_empty, W_v)
			}

			P_tree := make([]int, len(P_non_empty))
			copy(P_tree, P_non_empty)
			T_size := len(comp)
			for len(P_tree) <= T_size {
				P_tree = append(P_tree, 0)
			}
			P_tree[T_size] = add(P_tree[T_size], W_empty)

			F = poly_mul(F, P_tree)
		}
	}

	for k := 0; k <= n; k++ {
		ans := 0
		if k < len(F) {
			ans = mul(F[k], fact[k])
		}
		fmt.Printf("%d", ans)
		if k < n {
			fmt.Printf(" ")
		}
	}
	fmt.Println()
}