Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

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

Sample Output 1

999999999999998
999999999999989
999999999999979
999999999999897

After 0 years, it is optimal to do the exchange in City 1.

After 1 years, it is optimal to do the exchange in City 2.

Note that City 1 can still be visited even after the exchange office is closed.
Also note that, if it was allowed to keep 1 yen when do the exchange in City 2 and change the remaining yen into snuuk, we could reach City 3 with 999999999999998 snuuk, but this is NOT allowed.

After 2 years, it is optimal to do the exchange in City 3.

After 3 years, it is optimal to do the exchange in City 4.
Note that the same train can be used multiple times.

Sample Input 2

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

Sample Output 2

999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994

Solution in C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			var nmst = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
			int n = nmst[0];
			int m = nmst[1];
			int s = nmst[2] - 1;
			int t = nmst[3] - 1;

			var to = new List<Edge>[n];
			for (int i = 0; i < n; i++) {
				to[i] = new List<Edge>();
			}

			for (int i = 0; i < m; i++) {
				var temp = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
				int u = temp[0] - 1;
				int v = temp[1] - 1;
				long yen = temp[2];
				long snuke = temp[3];

				to[u].Add(new Edge { To = v, Yen = yen, Snuke = snuke });
				to[v].Add(new Edge { To = u, Yen = yen, Snuke = snuke });
			}

			long[] dYen = new long[n];
			long[] dSnuke = new long[n];

			{
				for (int i = 0; i < n; i++) {
					dYen[i] = long.MaxValue;
				}

				dYen[s] = 0;

				var q = new PriorityQueue<P>((x, y) => x.Cost.CompareTo(y.Cost), true);
				q.Enqueue(new P { V = s, Cost = 0 });
				while (q.Count > 0) {
					var cur = q.Dequeue();
					if (cur.Cost > dYen[cur.V]) {
						continue;
					}

					foreach (var next in to[cur.V]) {
						if (dYen[next.To] > dYen[cur.V] + next.Yen) {
							dYen[next.To] = dYen[cur.V] + next.Yen;
							q.Enqueue(new P { V = next.To, Cost = dYen[next.To] });
						}
					}
				}
			}

			{
				for (int i = 0; i < n; i++) {
					dSnuke[i] = long.MaxValue;
				}

				dSnuke[t] = 0;

				var q = new PriorityQueue<P>((x, y) => x.Cost.CompareTo(y.Cost), true);
				q.Enqueue(new P { V = t, Cost = 0 });
				while (q.Count > 0) {
					var cur = q.Dequeue();
					if (cur.Cost > dSnuke[cur.V]) {
						continue;
					}

					foreach (var next in to[cur.V]) {
						if (dSnuke[next.To] > dSnuke[cur.V] + next.Snuke) {
							dSnuke[next.To] = dSnuke[cur.V] + next.Snuke;
							q.Enqueue(new P { V = next.To, Cost = dSnuke[next.To] });
						}
					}
				}
			}

			var ans = new long[n];
			var costs = new List<long>();
			long cost = 0;
			for (int i = n - 1; i >= 0; i--) {
				if (i == n - 1) {
					cost = dYen[i] + dSnuke[i];
				} else {
					cost = Math.Min(
						cost,
						 dYen[i] + dSnuke[i]);
				}

				ans[i] = 1000000000000000L - cost;
			}

			var sb = new StringBuilder();
			for (int i = 0; i < n; i++) {
				sb.AppendLine(ans[i].ToString());
			}

			Console.Write(sb.ToString());
		}
	}

	public struct P
	{
		public int V { get; set; }
		public long Cost { get; set; }
	}

	public class Edge
	{
		public int To { get; set; }
		public long Yen { get; set; }

		public long Snuke { get; set; }
	}

	public class PriorityQueue<T>
	{
		public List<T> heap_;
		private readonly Comparison<T> comparison_;
		private readonly bool reverses_;

		public T Top => heap_[0];
		public int Count => heap_.Count;

		public PriorityQueue(bool reverses = false)
			: this(Comparer<T>.Default, reverses) { }

		public PriorityQueue(int capacity, bool reverses = false)
			: this(capacity, Comparer<T>.Default.Compare, reverses) { }

		public PriorityQueue(IComparer<T> comparer, bool reverses = false)
			: this(16, comparer.Compare, reverses) { }

		public PriorityQueue(Comparison<T> comparison, bool reverses = false)
			: this(16, comparison, reverses) { }

		public PriorityQueue(
			int capacity,
			Comparison<T> comparison,
			bool reverses = false)
		{
			heap_ = new List<T>(capacity);
			comparison_ = comparison;
			reverses_ = reverses;
		}

		public void Enqueue(T item)
		{
			int c = heap_.Count;
			heap_.Add(item);
			while (c > 0) {
				int p = (c - 1) >> 1;
				if (Compare(p, c) > 0) {
					Swap(p, c);
				} else {
					break;
				}

				c = p;
			}
		}

		public T Dequeue()
		{
			T ret = heap_[0];
			int n = heap_.Count - 1;

			heap_[0] = heap_[n];
			heap_.RemoveAt(n);
			for (int p = 0, c; (c = (p << 1) + 1) < n; p = c) {
				if (c != n - 1 && Compare(c + 1, c) < 0) {
					++c;
				}

				if (Compare(p, c) > 0) {
					Swap(p, c);
				} else {
					break;
				}
			}

			return ret;
		}

		private int Compare(int x, int y)
			=> comparison_(heap_[x], heap_[y]) * (reverses_ ? -1 : 1);

		private void Swap(int x, int y)
		{
			var t = heap_[x];
			heap_[x] = heap_[y];
			heap_[y] = t;
		}
	}

	public class UnionFindTree
	{
		private readonly List<int> sizes_;
		private readonly List<int> parents_;

		public int Count { get; private set; }
		public int GroupCount { get; private set; }

		public UnionFindTree(int count)
		{
			parents_ = new List<int>(count);
			sizes_ = new List<int>(count);

			Count = 0;
			GroupCount = 0;

			ExtendSize(count);
		}

		public bool IsUnited(int x, int y)
		{
			int xRoot = Find(x);
			int yRoot = Find(y);

			return xRoot == yRoot;
		}

		public bool TryUnite(int x, int y)
		{
			int xRoot = Find(x);
			int yRoot = Find(y);
			if (yRoot == xRoot) {
				return false;
			}

			int parent = sizes_[xRoot] < sizes_[yRoot] ? yRoot : xRoot;
			int child = sizes_[xRoot] < sizes_[yRoot] ? xRoot : yRoot;

			GroupCount--;
			parents_[child] = parent;
			sizes_[parent] += sizes_[child];

			return true;
		}
		public IEnumerable<int> AllRepresents => parents_.Where(x => x == parents_[x]);
		public int GetSize(int x) => sizes_[Find(x)];

		public int Find(int x)
		{
			while (x != parents_[x]) {
				parents_[x] = parents_[parents_[x]];
				x = parents_[x];
			}

			return x;
		}

		public void ExtendSize(int treeSize)
		{
			if (treeSize <= Count) {
				return;
			}

			parents_.Capacity = treeSize;
			sizes_.Capacity = treeSize;
			while (Count < treeSize) {
				parents_.Add(Count);
				sizes_.Add(1);
				Count++;
				GroupCount++;
			}
		}
	}
}