Problem:
Score : 500 points

Problem Statement

There are N cities numbered 1 to N, connected by M railroads.

You are now at City 1, with 10^{100} gold coins and S silver coins in your pocket.

The i-th railroad connects City U_i and City V_i bidirectionally, and a one-way trip costs A_i silver coins and takes B_i minutes.
You cannot use gold coins to pay the fare.

There is an exchange counter in each city. At the exchange counter in City i, you can get C_i silver coins for 1 gold coin.
The transaction takes D_i minutes for each gold coin you give.
You can exchange any number of gold coins at each exchange counter.

For each t=2, ..., N, find the minimum time needed to travel from City 1 to City t. You can ignore the time spent waiting for trains.

Constraints

2 \leq N \leq 50

N-1 \leq M \leq 100

0 \leq S \leq 10^9

1 \leq A_i \leq 50

1 \leq B_i,C_i,D_i \leq 10^9

1 \leq U_i < V_i \leq N

There is no pair i, j(i \neq j) such that (U_i,V_i)=(U_j,V_j).

Each city t=2,...,N can be reached from City 1 with some number of railroads.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M S
U_1 V_1 A_1 B_1
:
U_M V_M A_M B_M
C_1 D_1
:
C_N D_N

Output

For each t=2, ..., N in this order, print a line containing the minimum time needed to travel from City 1 to City t.

Sample Input 1

3 2 1
1 2 1 2
1 3 2 4
1 11
1 2
2 5

Sample Output 1

2
14

The railway network in this input is shown in the figure below.

In this figure, each city is labeled as follows:

The first line: the ID number i of the city (i for City i)

The second line: C_i / D_i

Similarly, each railroad is labeled as follows:

The first line: the ID number i of the railroad (i for the i-th railroad in input)

The second line: A_i / B_i

You can travel from City 1 to City 2 in 2 minutes, as follows:

Use the 1-st railroad to move from City 1 to City 2 in 2 minutes.

You can travel from City 1 to City 3 in 14 minutes, as follows:

Use the 1-st railroad to move from City 1 to City 2 in 2 minutes.

At the exchange counter in City 2, exchange 3 gold coins for 3 silver coins in 6 minutes.

Use the 1-st railroad to move from City 2 to City 1 in 2 minutes.

Use the 2-nd railroad to move from City 1 to City 3 in 4 minutes.

Sample Input 2

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

Sample Output 2

5
5
7

The railway network in this input is shown in the figure below:

You can travel from City 1 to City 4 in 7 minutes, as follows:

At the exchange counter in City 1, exchange 2 gold coins for 6 silver coins in 2 minutes.

Use the 2-nd railroad to move from City 1 to City 3 in 4 minutes.

Use the 4-th railroad to move from City 3 to City 4 in 1 minutes.

Sample Input 3

6 5 1
1 2 1 1
1 3 2 1
2 4 5 1
3 5 11 1
1 6 50 1
1 10000
1 3000
1 700
1 100
1 1
100 1

Sample Output 3

1
9003
14606
16510
16576

The railway network in this input is shown in the figure below:

You can travel from City 1 to City 6 in 16576 minutes, as follows:

Use the 1-st railroad to move from City 1 to City 2 in 1 minute.

At the exchange counter in City 2, exchange 3 gold coins for 3 silver coins in 9000 minutes.

Use the 1-st railroad to move from City 2 to City 1 in 1 minute.

Use the 2-nd railroad to move from City 1 to City 3 in 1 minute.

At the exchange counter in City 3, exchange 8 gold coins for 8 silver coins in 5600 minutes.

Use the 2-nd railroad to move from City 3 to City 1 in 1 minute.

Use the 1-st railroad to move from City 1 to City 2 in 1 minute.

Use the 3-rd railroad to move from City 2 to City 4 in 1 minute.

At the exchange counter in City 4, exchange 19 gold coins for 19 silver coins in 1900 minutes.

Use the 3-rd railroad to move from City 4 to City 2 in 1 minute.

Use the 1-st railroad to move from City 2 to City 1 in 1 minute.

Use the 2-nd railroad to move from City 1 to City 3 in 1 minute.

Use the 4-th railroad to move from City 3 to City 5 in 1 minute.

At the exchange counter in City 5, exchange 63 gold coins for 63 silver coins in 63 minutes.

Use the 4-th railroad to move from City 5 to City 3 in 1 minute.

Use the 2-nd railroad to move from City 3 to City 1 in 1 minute.

Use the 5-th railroad to move from City 1 to City 6 in 1 minute.

Sample Input 4

4 6 1000000000
1 2 50 1
1 3 50 5
1 4 50 7
2 3 50 2
2 4 50 4
3 4 50 3
10 2
4 4
5 5
7 7

Sample Output 4

1
3
5

The railway network in this input is shown in the figure below:

Sample Input 5

2 1 0
1 2 1 1
1 1000000000
1 1

Sample Output 5

1000000001

The railway network in this input is shown in the figure below:

You can travel from City 1 to City 2 in 1000000001 minutes, as follows:

At the exchange counter in City 1, exchange 1 gold coin for 1 silver coin in 1000000000 minutes.

Use the 1-st railroad to move from City 1 to City 2 in 1 minute.

Solution in C# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.IO;
using System.Reflection;
using static System.Math;
using System.Numerics;
static class Program{
	const int mod=(int)1e9+7;
	const long inf=long.MaxValue-1;
	static List<Tuple<int,int,int>>[] li;
	static void Main(){
		Sc sc=new Sc();
		var s=sc.Ia;
		int n=s[0],m=s[1];
		li=new List<Tuple<int,int,int>>[n+1];
		var b=new bool[n+1][];
		var c=new long[n+1][];
		const int g=50*50;
		for(int i=1;i<=n;i++){
			li[i]=new List<Tuple<int,int,int>>();
			c[i]=Enumerable.Repeat(inf,g+1).ToArray();
			b[i]=new bool[g+1];
		}
		for(int i=0;i<m;i++){
			var e=sc.Ia;
			li[e[0]].Add(Tuple.Create(e[1],e[3],e[2]));
			li[e[1]].Add(Tuple.Create(e[0],e[3],e[2]));
		}
		var a=new long[n+1][];
		for(int i = 1;i<=n;i++) {a[i]=sc.La;}
		var pq=new Rheap<Tuple<int,int>>(32);
		pq.Push(new Rheap<Tuple<int,int>>.Dt(0,Tuple.Create(1,Min(s[2],g))));
		var ans=new long[n-1];
		int z=0;
		while(pq.cnt>0){
			var e=pq.Dequeue;
			if(b[e.d.Item1][e.d.Item2]){continue;}
			b[e.d.Item1][e.d.Item2]=true;
			if(e.d.Item1!=1&&ans[e.d.Item1-2]==0){
				ans[e.d.Item1-2]=e.n;
				z++;
				if(z==n-1){break;}
			}
			for(int i = 1;;i++) {
				int p=(int)Min(e.d.Item2+i*a[e.d.Item1][0],g);
				if(!b[e.d.Item1][p]||c[e.d.Item1][p]>e.n+i*a[e.d.Item1][1]){
					pq.Push(new Rheap<Tuple<int,int>>.Dt(e.n+i*a[e.d.Item1][1],Tuple.Create(e.d.Item1,p)));
					c[e.d.Item1][p]=e.n+i*a[e.d.Item1][1];
				}
				else{break;}
				if(p==g){break;}
			}
			for(int i=0;i<li[e.d.Item1].Count;i++){
				if(li[e.d.Item1][i].Item3>e.d.Item2){continue;}
				if(!b[li[e.d.Item1][i].Item1][e.d.Item2-li[e.d.Item1][i].Item3]&&c[li[e.d.Item1][i].Item1][e.d.Item2-li[e.d.Item1][i].Item3]>li[e.d.Item1][i].Item2+e.n){
					pq.Push(new Rheap<Tuple<int,int>>.Dt(li[e.d.Item1][i].Item2+e.n,Tuple.Create(li[e.d.Item1][i].Item1,e.d.Item2-li[e.d.Item1][i].Item3)));
					c[li[e.d.Item1][i].Item1][e.d.Item2-li[e.d.Item1][i].Item3]=li[e.d.Item1][i].Item2+e.n;
				}
			}
		}
		Console.WriteLine("{0}",String.Join("\n",ans));
	}
}
public class Rheap<T>{
	public class Dt{
		public long n;
		public T d;
		public Dt(long n,T d){this.n=n;this.d=d;}
		public override string ToString()=>"d:"+d.ToString()+" n:"+n.ToString();
	}
	private const int m=65;
	private long la=0;
	private Dt[][] bf;
	private int[] h;
	public int cnt=0;
	public Rheap(int max){
		bf=new Dt[m][];
		h=new int[m];
		for(int i = 0;i<m;i++) {bf[i]=new Dt[max];}
	}
	public void Push(Dt x){
		int a=x.n!=la?Bsr(la^x.n)+1:0;
		if(h[a]==bf[a].Length){Extend(a);}
		bf[a][h[a]]=x;
		cnt++;
		h[a]++;
	}
	public Dt Peek{get{
		if(h[0]==0){
			for(int i = 1;i<m;i++) {
				if(h[i]>0){
					int p=0;
					for(int j = 1;j<h[i];j++) {
						if(bf[i][p].n>bf[i][j].n){p=j;}
					}
					la=bf[i][p].n;
					for(int j = 0;j<h[i];j++) {
						Push(bf[i][j]);
						cnt--;
					}
					h[i]=0;
					break;
				}
			}
		}
		return bf[0][h[0]-1];
	}}
	public Dt Dequeue{get{
		var e=Peek;
		h[0]--;
		cnt--;
		return e;
	}}
	private void Extend(int n){
		var nhe=new Dt[bf[n].Length<<1];
		Array.Copy(bf[n],nhe,bf[n].Length);
		bf[n]=nhe;
	}
	private int Bsr(long b){
		int n=0;
		if(b==0){return -1;}
		if((b&-4294967296)!=0){b=b&-4294967296;n+=32;}
		if((b&-281470681808896)!=0){b=b&-281470681808896;n+=16;}
		if((b&-71777214294589696)!=0){b=b&-71777214294589696;n+=8;}
		if((b&-1085102592571150096)!=0){b=b&-1085102592571150096;n+=4;}
		if((b&-3689348814741910324)!=0){b=b&-3689348814741910324;n+=2;}
		if((b&-6148914691236517206)!=0){b=b&-6148914691236517206;n+=1;}
		return n;
	}
}
public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
	public object[] Oa{get{return Console.ReadLine().Split();}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),int.Parse);}}
	public int[] Ia3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),int.Parse);}
	public int[] Ia3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),int.Parse);}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),long.Parse);}}
	public long[] La3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),long.Parse);}
	public long[] La3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),long.Parse);}
	public double[] Da2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),double.Parse);}}
	public double[] Da3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),double.Parse);}
	public double[] Da3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),double.Parse);}
	public T[] Arr<T>(int n,Func<T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f();}return a;}
	public T[] Arr<T>(int n,Func<int,T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i);}return a;}
	public T[] Arr<T>(int n,Func<string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(Console.ReadLine().Split());}return a;}
	public T[] Arr<T>(int n,Func<int,string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i,Console.ReadLine().Split());}return a;}
}