Kenkoooo is planning a trip in Republic of Snuke. In this country, there are n cities and m trains running. The cities are numbered 1 through n, and the i-th train connects City u_i and v_i bidirectionally. Any city can be reached from any city by changing trains.

Two currencies are used in the country: yen and snuuk. Any train fare can be paid by both yen and snuuk. The fare of the i-th train is a_i yen if paid in yen, and b_i snuuk if paid in snuuk.

In a city with a money exchange office, you can change 1 yen into 1 snuuk. However, when you do a money exchange, you have to change all your yen into snuuk. That is, if Kenkoooo does a money exchange when he has X yen, he will then have X snuuk. Currently, there is a money exchange office in every city, but the office in City i will shut down in i years and can never be used in and after that year.

Kenkoooo is planning to depart City s with 10^{15} yen in his pocket and head for City t, and change his yen into snuuk in some city while traveling. It is acceptable to do the exchange in City s or City t.

Kenkoooo would like to have as much snuuk as possible when he reaches City t by making the optimal choices for the route to travel and the city to do the exchange. For each i=0,...,n-1, find the maximum amount of snuuk that Kenkoooo has when he reaches City t if he goes on a trip from City s to City t after i years. You can assume that the trip finishes within the year.

Constraints

* 2 \leq n \leq 10^5
* 1 \leq m \leq 10^5
* 1 \leq s,t \leq n
* s \neq t
* 1 \leq u_i < v_i \leq n
* 1 \leq a_i,b_i \leq 10^9
* If i\neq j, then u_i \neq u_j  or v_i \neq v_j.
* Any city can be reached from any city by changing trains.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


n m s t
u_1 v_1 a_1 b_1
:
u_m v_m a_m b_m


Output

Print n lines. In the i-th line, print the maximum amount of snuuk that Kenkoooo has when he reaches City t if he goes on a trip from City s to City t after i-1 years.

Examples

Input

4 3 2 3
1 4 1 100
1 2 1 10
1 3 20 1


Output

999999999999998
999999999999989
999999999999979
999999999999897


Input

8 12 3 8
2 8 685087149 857180777
6 7 298270585 209942236
2 4 346080035 234079976
2 5 131857300 22507157
4 8 30723332 173476334
2 6 480845267 448565596
1 4 181424400 548830121
4 5 57429995 195056405
7 8 160277628 479932440
1 6 475692952 203530153
3 5 336869679 160714712
2 7 389775999 199123879


Output

999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
import java.io.IOException; 
import java.io.InputStream; 
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.PriorityQueue; 

class Main{

	static class Edge{
		int to;
		long ca,cb;
		Edge(int t, long ca, long cb){to=t;this.ca=ca;this.cb=cb;}
	}
	static class Node{
		int to;
		long cost;
		Node(int t, long c){to=t;cost=c;}
	}

	static void solve(){ 
		int n=ni(), m=ni(), s=ni()-1, t=ni()-1;
		List<Edge> edges[] = new ArrayList[n];
		for(int i=0;i<n;++i)edges[i]=new ArrayList<>();
		while(m-->0){
			int u=ni()-1, v=ni()-1, a=ni(), b=ni();
			edges[u].add(new Edge(v, a, b));
			edges[v].add(new Edge(u, a, b));
		}
		long[] disa = new long[n];
		long[] disb = new long[n];
		Arrays.fill(disa, Long.MAX_VALUE);
		disa[s]=0;
		Arrays.fill(disb, Long.MAX_VALUE);
		disb[t]=0;
		PriorityQueue<Node> que = new PriorityQueue<>((a,b)->a.cost-b.cost<0 ? -1:1);
		que.add(new Node(s, 0));
		while(!que.isEmpty()){
			Node node = que.poll();
			if(disa[node.to]< node.cost)continue;
			for(Edge e: edges[node.to]){
				if(disa[e.to]>node.cost+e.ca){
					disa[e.to]=node.cost+e.ca;
					que.add(new Node(e.to, disa[e.to]));
				}
			}
		}
		que.add(new Node(t, 0));
		while(!que.isEmpty()){
			Node node = que.poll();
			if(disb[node.to]< node.cost)continue;
			for(Edge e: edges[node.to]){
				if(disb[e.to]> node.cost+e.cb){
					disb[e.to]=node.cost+e.cb;
					que.add(new Node(e.to, disb[e.to]));
				}
			}
		}
		long[] ans = new long[n];
		ans[n-1]=disa[n-1]+disb[n-1];
		for(int i=n-2;i>=0;--i)ans[i]=Math.min(ans[i+1], disa[i]+disb[i]);
		for(int i=0;i<n;++i)System.out.println((long)1e15-ans[i]);
	} 
 
 
 
 
	public static void main(String[] args){ 
		 solve(); 
		 out.flush(); 
	 } 
	 private static InputStream in = System.in; 
	 private static PrintWriter out = new PrintWriter(System.out); 
 
	 private static final byte[] buffer = new byte[1<<15]; 
	 private static int ptr = 0; 
	 private static int buflen = 0; 
	 private static boolean hasNextByte(){ 
		 if(ptr<buflen)return true; 
		 ptr = 0; 
		 try{ 
			 buflen = in.read(buffer); 
		 } catch (IOException e){ 
			 e.printStackTrace(); 
		 } 
		 return buflen>0; 
	 } 
	 private static int readByte(){ if(hasNextByte()) return buffer[ptr++]; else return -1;} 
	 private static boolean isSpaceChar(int c){ return !(33<=c && c<=126);} 
	 private static int skip(){int res; while((res=readByte())!=-1 && isSpaceChar(res)); return res;} 
 
	 private static double nd(){ return Double.parseDouble(ns()); } 
	 private static char nc(){ return (char)skip(); } 
	 private static String ns(){ 
		 StringBuilder sb = new StringBuilder(); 
		 for(int b=skip();!isSpaceChar(b);b=readByte())sb.append((char)b); 
		 return sb.toString(); 
	 } 
	 private static int[] nia(int n){ 
		 int[] res = new int[n]; 
		 for(int i=0;i<n;++i)res[i]=ni(); 
		 return res; 
	 } 
	 private static long[] nla(int n){ 
		 long[] res = new long[n]; 
		 for(int i=0;i<n;++i)res[i]=nl(); 
		 return res; 
	 } 
	 private static int ni(){ 
		 int res=0,b; 
		 boolean minus=false; 
		 while((b=readByte())!=-1 && !((b>='0'&&b<='9') || b=='-')); 
		 if(b=='-'){ 
			 minus=true; 
			 b=readByte(); 
		 } 
		 for(;'0'<=b&&b<='9';b=readByte())res=res*10+(b-'0'); 
		 return minus ? -res:res; 
	 } 
	 private static long nl(){ 
		 long res=0,b; 
		 boolean minus=false; 
		 while((b=readByte())!=-1 && !((b>='0'&&b<='9') || b=='-')); 
		 if(b=='-'){ 
			 minus=true; 
			 b=readByte(); 
		 } 
		 for(;'0'<=b&&b<='9';b=readByte())res=res*10+(b-'0'); 
		 return minus ? -res:res; 
	} 
} 

