Problem: Constraints

* 1 ≤ |V| ≤ 1000
* 0 ≤ |E| ≤ 2000
* -10000 ≤ di ≤ 10000
* There are no parallel edges
* There are no self-loops

Input

An edge-weighted graph G (V, E) and the source r.


|V| |E| r
s0 t0 d0
s1 t1 d1
:
s|E|-1 t|E|-1 d|E|-1


|V| is the number of vertices and |E| is the number of edges in G. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively. r is the source of the graph.

si and ti represent source and target vertices of i-th edge (directed) and di represents the cost of the i-th edge.

Output

If the graph contains a negative cycle (a cycle whose sum of edge costs is a negative value) which is reachable from the source r, print


NEGATIVE CYCLE


in a line.

Otherwise, print


c0
c1
:
c|V|-1


The output consists of |V| lines. Print the cost of the shortest path from the source r to each vertex 0, 1, ... |V|-1 in order. If there is no path from the source to a vertex, print "INF".

Examples

Input

4 5 0
0 1 2
0 2 3
1 2 -5
1 3 1
2 3 2


Output

0
2
-3
-1


Input

4 6 0
0 1 2
0 2 3
1 2 -5
1 3 1
2 3 2
3 1 0


Output

NEGATIVE CYCLE


Input

4 5 1
0 1 2
0 2 3
1 2 -5
1 3 1
2 3 2


Output

INF
0
-5
-3

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;
import java.util.NoSuchElementException;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.TreeSet;
 
 
public class Main {
 
	static long MOD = 1_000_000_007;
	//static int INF = 1_000_000_007;
	static long INF = Long.MAX_VALUE;
	//二項係数関連ここから-----
	static boolean isPreprocessing = false;	//二項係数を計算するための前処理を行っているかどうかのフラグ
	static int MAX = 260;				//MAXまで階乗やそれらの逆元のテーブルを保持する。
	static long[] fac;	//fac[i] := i! % MOD
	static long[] inv;	//inv[i] := mod. MODにおける i の逆元
	static long[] finv;	//finv[i] := mod. MODにおける i! の逆元(invの累積"積")
	//二項係数関連おわり------
	
	static int[] roots;		//Union-find木用
	static int[] ans;
	//static List<ArrayList<Integer>> G;	//グラフ用

	static List<List<E>> G = new ArrayList<>();	//グラフ用
	static List<E> Edges = new ArrayList<>();	//グラフ用
	static int V;								//グラフ用頂点の数
	static int E;								//グラフ用辺の数
	
	
	public static void main(String[] args) throws Exception {
		FastScanner scan = new FastScanner();
		//int N = scan.nextInt();
		//long L = scan.nextLong();
		//char[] A = scan.next().toCharArray();
		
		V = scan.nextInt();
		E = scan.nextInt();
		int r = scan.nextInt();
		//for(int i=0; i<V; i++)G.add(new ArrayList<E>());
		for(int i=0; i<E; i++){
			int s = scan.nextInt();
			int t = scan.nextInt();
			int d = scan.nextInt();
			Edges.add(new E(s,t,d));
		}
		long[] ans = bellmanFord(Edges, r);
		if(ans[V] == -1){
			System.out.println("NEGATIVE CYCLE");
		}else{
			for(int i=0; i<V; i++){
				System.out.println((ans[i] == INF) ? "INF": ans[i]);
			}
		}
	}
	
	
	//Bellman-Ford法
	//辺情報とstartの頂点を指定すると、すべての頂点への最短コストを返す（負の重みの辺もOK）
	//負の閉路がある場合はindex:Vの要素に-1を入れて返す。
	static long[] bellmanFord(List<E> Edges, int from){
		long[] rtn = new long[V+1];
		Arrays.fill(rtn, INF);
		rtn[from] = 0;
		int count = 0;
		while(true){
			count++;
			if(count>V){
				rtn[V] = -1;
				break;
			}
			boolean update = false;
			for(E e : Edges){
				if(rtn[e.from] != INF && rtn[e.to] > rtn[e.from] + e.weight){
					rtn[e.to] = rtn[e.from] + e.weight;
					update = true;
				}
			}
			if(!update)break;
		}	
		return rtn;
	}
	
	//Kruskal法
	//最小全域木を構成したときのコストの総和を返す
	static long kruskal(List<E> Edges){
		Collections.sort(Edges);
		UnionFind uni = new UnionFind(V);
		long res = 0L;
		for (E e : Edges){
			if(!uni.same(e.from, e.to)){
				uni.join(e.from, e.to);
				res += e.weight;
			}
		}
		return res;
	}
	
	//Dijkstra法
	//辺情報とstartの頂点を指定すると、すべての頂点への最短コストを返す
	static long[] dijkstra(List<List<E>> G, int from){
		int N = G.size();
		long[] rtn = new long[N];
		Arrays.fill(rtn, INF);
		rtn[from] = 0;
		Queue<V> que = new PriorityQueue<>();
		
		que.add(new V(from,0));
        while(!que.isEmpty()){
            V doneNode = que.poll();
            for(E e: G.get(doneNode.num)){
                  long alt = rtn[doneNode.num] + e.weight;
                  if(rtn[e.to] > alt){
                        rtn[e.to] = alt;
                        que.add(new V(e.to, alt));
                  }     
            }
        }
		return rtn;
	}
	
	//グラフ用：辺
	static class E implements Comparable<E>{
		int from;
		int to;
		long weight;
		public E(int from, int to, long weight){
			this.from = from;
			this.to = to;
			this.weight = weight;
		}
		@Override
		public int compareTo(E o) {
			// TODO Auto-generated method stub
			return Long.compare(this.weight, o.weight);
		}
	}
	//グラフ用：頂点
	static class V implements Comparable<V>{
		int num;
		long cost;
		public V(int num, long cost){
			this.num = num;
			this.cost = cost;
		}
		//コストの低い順に並べる(PriorityQueue用)
		@Override
		public int compareTo(V o) {
			return Long.compare(this.cost, o.cost);
		}
	}
	
	//Union-Find木
	static class UnionFind{
		private int[] roots;
		public UnionFind(int N){
			this.roots = new int[N];
			for(int i=0; i<N; i++){
				this.roots[i] = i;
			}
		}
		
		public boolean same(int a, int b){
			if(root(a) == root(b)){
				return true;
			}else{
				return false;
			}
		}
		
		public int root(int a){
			if(a == this.roots[a])return a;
			return this.roots[a] = root(this.roots[a]);
		}
		
		public void join(int a, int b){
			if(root(a) == root(b))return;
			this.roots[root(b)] = root(a);
		}
		
		public int[] getRoots(){
			return this.roots;
		}
	}
 
	//素因数分解をする(index_0:素数 index_1:個数)
	static List<long[]> factorization(long M){
		List<long[]> primes = new ArrayList<>();
 
		long now_prime = 2;
		long now_M = M;
		while(now_prime*now_prime<=M){
			if(now_M%now_prime == 0){
				now_M /= now_prime;
				long[] prime = new long[2];
				prime[0] = now_prime;
				prime[1] = 1;
				while(now_M%now_prime == 0){
					now_M /= now_prime;
					prime[1]++;
				}
				primes.add(prime);
				
			}
			if(now_prime%2 == 0){
				now_prime++;
			}else{
				now_prime += 2;
			}
		}
		if (now_M>1 || M==1){
			long[] prime = new long[2];
			prime[0] = now_M;
			prime[1] = 1;
			primes.add(prime);
		}
		
		return primes;
	}
	
	//２つのint配列を連結させる
	static int[] joinArray(int[] A, int[] B){
		int[] tmp = new int[A.length + B.length];
		System.arraycopy(A, 0, tmp, 0, A.length);
		System.arraycopy(B, 0, tmp, A.length, B.length);
		return tmp;
	}
	
	//２つのint配列が等しいかどうか判定する
	static boolean arrayEqual(int[] A, int[] B){
		if(A.length != B.length)return false;
		for(int i=0; i<A.length; i++){
			if(A[i] != B[i])return false;
		}
		return true;
	}
	
	//int配列をindex順に見て、要素の重複があった場合その要素と間の要素を削除する12123→23
	static int[] calc(int[] A){
		boolean[] tmp = new boolean[A.length];
		Arrays.fill(tmp, true);
		int fetch = 0;
		while(fetch<A.length-1){
			boolean isExist = false;
			for(int i=fetch+1; i<A.length;i++){
				if(A[fetch] == A[i]){
					for(int j=fetch;j<=i;j++){
						tmp[j]=false;
					}
					fetch = i+1;
					isExist = true;
					break;
				}
			}
			if(!isExist)fetch++;
		}
		List<Integer> list = new ArrayList<>();
		for(int i=0; i<A.length; i++){
			if(tmp[i])list.add(A[i]);
		}
		
		int[] foo = new int[list.size()];
		for(int i=0; i<list.size(); i++){
			foo[i] = list.get(i);
		}
		/*
		for(boolean t : tmp)
			System.out.print(t+" ");
		*/
		return foo;
	}
	
	
	//aとbの最小公倍数を返す
	static long lcm (long a, long b) {
		long temp;
		long c = a;
		c *= b;
		while((temp = a%b)!=0) {
			a = b;
			b = temp;
		}
		return (c/b);
	}
	
	//二項係数用の前処理
	static void COMinit(){
		//二項係数演算用前処理
		fac = new long[MAX+1];
		fac[0] = 1L;
		fac[1] = 1L;
		inv = new long[MAX+1];
		inv[1] = 1L;
		finv = new long[MAX+1];
		finv[0] = 1L;
		finv[1] = 1L;
		for(int i=2;i<MAX;i++){
			fac[i] = fac[i-1] * i % MOD;
			inv[i] = MOD - inv[(int)(MOD%i)] * (MOD/i) % MOD;
			finv[i] = finv[i-1] * inv[i] % MOD;
		}
		isPreprocessing = true;
	}
	
	//二項係数i_C_jをMODで割った余りを返す
	static long COM(int i, int j){
		if(i<j)return 0;
		if(i<0 || j<0)return 0;
		if(!isPreprocessing)COMinit();
		return fac[i] * (finv[j] * finv[i-j] % MOD) % MOD;
	}
	
	//入力
	//https://qiita.com/p_shiki37/items/a0f6aac33bf60f5f65e4
	static class FastScanner {
	    private final InputStream in = System.in;
	    private final byte[] buffer = new byte[1024];
	    private int ptr = 0;
	    private int buflen = 0;
	    private boolean hasNextByte() {
	        if (ptr < buflen) {
	            return true;
	        }else{
	            ptr = 0;
	            try {
	                buflen = in.read(buffer);
	            } catch (IOException e) {
	                e.printStackTrace();
	            }
	            if (buflen <= 0) {
	                return false;
	            }
	        }
	        return true;
	    }
	    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
	    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
	    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
	    public String next() {
	        if (!hasNext()) throw new NoSuchElementException();
	        StringBuilder sb = new StringBuilder();
	        int b = readByte();
	        while(isPrintableChar(b)) {
	            sb.appendCodePoint(b);
	            b = readByte();
	        }
	        return sb.toString();
	    }
	    public long nextLong() {
	        if (!hasNext()) throw new NoSuchElementException();
	        long n = 0;
	        boolean minus = false;
	        int b = readByte();
	        if (b == '-') {
	            minus = true;
	            b = readByte();
	        }
	        if (b < '0' || '9' < b) {
	            throw new NumberFormatException();
	        }
	        while(true){
	            if ('0' <= b && b <= '9') {
	                n *= 10;
	                n += b - '0';
	            }else if(b == -1 || !isPrintableChar(b)){
	                return minus ? -n : n;
	            }else{
	                throw new NumberFormatException();
	            }
	            b = readByte();
	        }
	    }
	    public int nextInt() {
	        long nl = nextLong();
	        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
	        return (int) nl;
	    }
	    public double nextDouble() { return Double.parseDouble(next());}
	}
}