Problem:
Score : 500 points

Problem Statement

There is a rooted tree (see Notes) with N vertices numbered 1 to N.
Each of the vertices, except the root, has a directed edge coming from its parent.
Note that the root may not be Vertex 1.

Takahashi has added M new directed edges to this graph.
Each of these M edges, u \rightarrow v, extends from some vertex u to its descendant v.

You are given the directed graph with N vertices and N-1+M edges after Takahashi added edges.
More specifically, you are given N-1+M pairs of integers, (A_1, B_1), ..., (A_{N-1+M}, B_{N-1+M}), which represent that the i-th edge extends from Vertex A_i to Vertex B_i.

Restore the original rooted tree.

Notes

For "tree" and other related terms in graph theory, see the article in Wikipedia, for example.

Constraints

3 \leq N

1 \leq M

N + M \leq 10^5

1 \leq A_i, B_i \leq N

A_i \neq B_i

If i \neq j, (A_i, B_i) \neq (A_j, B_j).

The graph in input can be obtained by adding M edges satisfying the condition in the problem statement to a rooted tree with N vertices.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
:
A_{N-1+M} B_{N-1+M}

Output

Print N lines.
In the i-th line, print 0 if Vertex i is the root of the original tree, and otherwise print the integer representing the parent of Vertex i in the original tree.

Note that it can be shown that the original tree is uniquely determined.

Sample Input 1

3 1
1 2
1 3
2 3

Sample Output 1

0
1
2

The graph in this input is shown below:

It can be seen that this graph is obtained by adding the edge 1 \rightarrow 3 to the rooted tree 1 \rightarrow 2 \rightarrow 3.

Sample Input 2

6 3
2 1
2 3
4 1
4 2
6 1
2 6
4 6
6 5

Sample Output 2

6
4
2
0
6
2

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#define dag_valtype int
#define graph_valtype int
typedef struct graph_edge_sub graph_edge;

typedef struct {
	int num;
	int next_num;
	graph_edge *next;
	int prev_num;
}graph_vertex_sub;

struct graph_edge_sub{
	graph_vertex_sub *v;
	int w;
	graph_edge *next;
};

typedef struct graph_v_sub graph_vertex;

struct graph_v_sub{
	int num;
	graph_valtype val;
	int next_num;
	graph_vertex **next;
	int *next_weight;
	int prev_num;
	graph_vertex **prev;
	int *prev_weight;
};

typedef struct {
	int N;
	graph_vertex_sub **v_s;
	graph_vertex **v;
}graph;

//頂点数N, 各頂点の初期値ini_valのグラフを作る
graph *make_graph(int N, graph_valtype ini_val){
	int i;
	graph *g = (graph *)malloc(sizeof(graph));
	g->N = N;
	g->v_s = (graph_vertex_sub **)malloc(sizeof(graph_vertex_sub *) * N);
	g->v = (graph_vertex **)malloc(sizeof(graph_vertex *) * N);
	for(i = 0; i < N; i++){
		(g->v_s)[i] = (graph_vertex_sub *)malloc(sizeof(graph_vertex_sub));
		(g->v_s)[i]->num = i;
		(g->v_s)[i]->next_num = 0;
		(g->v_s)[i]->next = NULL;
		(g->v_s)[i]->prev_num = 0;
		(g->v)[i] = (graph_vertex *)malloc(sizeof(graph_vertex));
		(g->v)[i]->num = i;
		(g->v)[i]->val = ini_val;
		(g->v)[i]->next_num = 0;
		(g->v)[i]->next = NULL;
		(g->v)[i]->next_weight = NULL;
		(g->v)[i]->prev_num = 0;
		(g->v)[i]->prev = NULL;
		(g->v)[i]->prev_weight = NULL;
	}
	return g;
}

//グラフgの頂点aから頂点bに重みwの有向辺を張る (0 <= a, b <= N - 1)
void set_edge_graph(int a, int b, int w, graph *g){
	graph_edge *new1 = (graph_edge *)malloc(sizeof(graph_edge));
	new1->v = (g->v_s)[b];
	new1->w = w;
	new1->next = (g->v_s)[a]->next;
	(g->v_s)[a]->next = new1;
	(g->v_s)[a]->next_num++;
	(g->v_s)[b]->prev_num++;
}

//set_edge_graph後に呼び出す
void build_graph(graph *g){
	int i;
	graph_vertex_sub **v_s = g->v_s;
	graph_vertex **v = g->v;
	graph_vertex *nowv;
	graph_edge *nowe;
	for(i = 0; i < g->N; i++){
		v[i]->next = (graph_vertex **)malloc(sizeof(graph_vertex *) * v_s[i]->next_num);
		v[i]->next_weight = (int *)malloc(sizeof(int) * v_s[i]->next_num);
		v[i]->prev = (graph_vertex **)malloc(sizeof(graph_vertex *) * v_s[i]->prev_num);
		v[i]->prev_weight = (int *)malloc(sizeof(int) * v_s[i]->prev_num);
	}
	for(i = 0; i < g->N; i++){
		nowv = v[i];
		for(nowe = v_s[i]->next; nowe != NULL; nowe = nowe->next){
			(nowv->next)[nowv->next_num] = v[nowe->v->num];
			(nowv->next_weight)[nowv->next_num] = nowe->w;
			nowv->next_num++;
			(v[nowe->v->num]->prev)[v[nowe->v->num]->prev_num] = nowv;
			(v[nowe->v->num]->prev_weight)[v[nowe->v->num]->prev_num] = nowe->w;
			v[nowe->v->num]->prev_num++;
		}
	}
}

typedef struct SCC_sub{
	int num; //強連結成分番号
	int vertex_num; //強連結成分に含まれる頂点の個数
	int *vertexs; //強連結成分に含まれる元のグラフでの頂点番号
	dag_valtype val;
	int next_num;
	struct SCC_sub **next;
	int *next_weight;
	int prev_num;
	struct SCC_sub **prev;
	int *prev_weight;
}SCC; //強連結成分(Strongly Connected Components)

typedef struct {
	int N;
	SCC **sorted_SCC; //topological sort済み
}DAG; //非閉路有向グラフ(Directed Acyclic Graph)

int dfs(int next_bt, int *used, int *bt, int *bt_inv, graph_vertex *v){
	if(used[v->num] == 1){
		return next_bt;
	}
	else{
		int i;
		used[v->num] = 1;
		for(i = 0; i < v->next_num; i++){
			next_bt = dfs(next_bt, used, bt, bt_inv, v->next[i]);
		}
		bt[v->num] = next_bt;
		bt_inv[next_bt] = v->num;
		return next_bt + 1;
	}
}

void dfs_rev1(int next_SCC_num, int *used, int *SCC_num, int *next_num, int *prev_num, graph_vertex *v){
	if(used[v->num] == 1){
		int i;
		used[v->num] = 2;
		for(i = 0; i < v->prev_num; i++){
			dfs_rev1(next_SCC_num, used, SCC_num, next_num, prev_num, v->prev[i]);
		}
		SCC_num[v->num] = next_SCC_num;
		for(i = 0; i < v->next_num; i++){
			if(used[v->next[i]->num] == 1){
				next_num[v->num]++;
				prev_num[v->next[i]->num]++; //ここで自己ループを数えてしまう可能性がある
			}
		}
	}
}

void dfs_rev2(SCC *now_SCC, int *used, int *SCC_num, graph_vertex *v, DAG *dag){
	if(used[v->num] == 2){
		int i;
		SCC *next_SCC;
		used[v->num] = 3;
		for(i = 0; i < v->prev_num; i++){
			dfs_rev2(now_SCC, used, SCC_num, v->prev[i], dag);
		}
		now_SCC->vertexs[now_SCC->vertex_num] = v->num;
		now_SCC->vertex_num++;
		for(i = 0; i < v->next_num; i++){
			if(used[v->next[i]->num] == 2){
				next_SCC = dag->sorted_SCC[SCC_num[v->next[i]->num]];
				if(now_SCC->num != next_SCC->num){ //自己ループがないようにしている
					now_SCC->next[now_SCC->next_num] = next_SCC;
					now_SCC->next_weight[now_SCC->next_num] = v->next_weight[i];
					now_SCC->next_num++;
					next_SCC->prev[next_SCC->prev_num] = now_SCC;
					next_SCC->prev_weight[next_SCC->prev_num] = v->next_weight[i];
					next_SCC->prev_num++;
				}
			}
		}
	}
}

DAG *build_DAG(graph *g, dag_valtype ini_val){
	int N = g->N, i;
	int *used = (int *)malloc(sizeof(int) * N);

	int *bt = (int *)malloc(sizeof(int) * N);
	int *bt_inv = (int *)malloc(sizeof(int) * N);
	for(i = 0; i < N; i++){
		used[i] = 0;
		bt[i] = -1;
		bt_inv[i] = -1;
	}
	int next_bt;
	for(i = 0, next_bt = 0; i < N; i++){
		next_bt = dfs(next_bt, used, bt, bt_inv, g->v[i]);
	}

	int *SCC_num = (int *)malloc(sizeof(int) * N);
	int *next_num = (int *)malloc(sizeof(int) * N);
	int *prev_num = (int *)malloc(sizeof(int) * N);
	for(i = 0; i < N; i++){
		SCC_num[i] = 0;
		next_num[i] = 0;
		prev_num[i] = 0;
	}
	int next_SCC_num;
	for(i = N - 1, next_SCC_num = 0; i >= 0; i--){
		if(used[bt_inv[i]] == 1){
			dfs_rev1(next_SCC_num, used, SCC_num, next_num, prev_num, g->v[bt_inv[i]]);
			next_SCC_num++;
		}
	}

	DAG *dag = (DAG *)malloc(sizeof(DAG));
	SCC *now_SCC;
	dag->N = next_SCC_num;
	dag->sorted_SCC = (SCC **)malloc(sizeof(SCC *) * dag->N);
	for(i = 0; i < dag->N; i++){
		dag->sorted_SCC[i] = (SCC *)malloc(sizeof(SCC));
		now_SCC = dag->sorted_SCC[i];
		now_SCC->num = i;
		now_SCC->vertex_num = 0;
		now_SCC->vertexs = NULL;
		now_SCC->val = ini_val;
		now_SCC->next_num = 0;
		now_SCC->next = NULL;
		now_SCC->next_weight = NULL;
		now_SCC->prev_num = 0;
		now_SCC->prev = NULL;
		now_SCC->prev_weight = NULL;
	}
	for(i = 0; i < N; i++){
		now_SCC = dag->sorted_SCC[SCC_num[i]];
		now_SCC->vertex_num++;
		now_SCC->next_num += next_num[i];
		now_SCC->prev_num += prev_num[i];
	}
	for(i = 0; i < dag->N; i++){
		now_SCC = dag->sorted_SCC[i];
		now_SCC->vertexs = (int *)malloc(sizeof(int) * now_SCC->vertex_num);
		now_SCC->next = (SCC **)malloc(sizeof(SCC *) * now_SCC->next_num);
		now_SCC->next_weight = (int *)malloc(sizeof(int) * now_SCC->next_num);
		now_SCC->prev = (SCC **)malloc(sizeof(SCC *) * now_SCC->prev_num);
		now_SCC->prev_weight = (int *)malloc(sizeof(int) * now_SCC->prev_num);
		now_SCC->vertex_num = 0;
		now_SCC->next_num = 0;
		now_SCC->prev_num = 0;
	}

	for(i = N - 1, next_SCC_num = 0; i >= 0; i--){
		if(used[bt_inv[i]] == 2){
			dfs_rev2(dag->sorted_SCC[next_SCC_num], used, SCC_num, g->v[bt_inv[i]], dag);
			next_SCC_num++;
		}
	}
	free(used);
	free(bt);
	free(bt_inv);
	free(SCC_num);
	free(next_num);
	free(prev_num);

	return dag;
}

int main(){
	int N, M, A, B, i, j;
	scanf("%d%d", &N, &M);
	graph *g = make_graph(N, 0);
	for(i = 0; i < N + M - 1; i++){
		scanf("%d%d", &A, &B);
		set_edge_graph(A - 1, B - 1, 1, g);
	}
	build_graph(g);
	DAG *dag = build_DAG(g, 0);
	for(i = 0; i < N; i++){
		dag->sorted_SCC[i]->val = N - 1 - i;
	}
	int minval, thennum;
	SCC *now_SCC;
	int *ans = (int *)malloc(sizeof(int) * N);
	for(i = N - 1; i > 0; i--){
		now_SCC = dag->sorted_SCC[i];
		minval = N;
		for(j = 0; j < now_SCC->prev_num; j++){
			if(now_SCC->prev[j]->val < minval){
				minval = now_SCC->prev[j]->val;
				thennum = now_SCC->prev[j]->vertexs[0];
			}
		}
		ans[now_SCC->vertexs[0]] = thennum;
	}
	ans[dag->sorted_SCC[0]->vertexs[0]] = -1;
	for(i = 0; i < N; i++){
		printf("%d\n", ans[i] + 1);
	}
	return 0;
}