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

Figure

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:

Figure

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:

Figure

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:

Figure

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:

Figure

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.