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 $t$.

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

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.

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

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.

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

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.

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

1
3
5

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

2 1 0
1 2 1 1
1 1000000000
1 1

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.