Two Currencies

AtCoder
IDabc164_e
Time2000ms
Memory256MB
Difficulty
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: $N$ $M$ $S$ $U_1$ $V_1$ $A_1$ $B_1$ $:$ $U_M$ $V_M$ $A_M$ $B_M$ $C_1$ $D_1$ $:$ $C_N$ $D_N$ [samples]
Samples
Input #1
3 2 1
1 2 1 2
1 3 2 4
1 11
1 2
2 5
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: $A_i$ / $B_i$

![image](https://img.atcoder.jp/ghi/83f6a1d296d017f40372ea1e1d3b26e5.png)
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.
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
Output #2
5
5
7

The railway network in this input is shown in the figure below:
![image](https://img.atcoder.jp/ghi/a081a72c42da7902a30f29f981c368d0.png)
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.
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
Output #3
1
9003
14606
16510
16576

The railway network in this input is shown in the figure below:
![image](https://img.atcoder.jp/ghi/c61c66a7977129c9ef86c6770b37acba.png)
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.
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
Output #4
1
3
5

The railway network in this input is shown in the figure below:
![image](https://img.atcoder.jp/ghi/bfbde2d55baea1e0487f80a62ef9b4ab.png)
Input #5
2 1 0
1 2 1 1
1 1000000000
1 1
Output #5
1000000001

The railway network in this input is shown in the figure below:
![image](https://img.atcoder.jp/ghi/16b8d5c94640ed5b38c0863716196890.png)
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.
API Response (JSON)
{
  "problem": {
    "name": "Two Currencies",
    "description": {
      "content": "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 $U_i$ ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc164_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ cities numbered $1$ to $N$, connected by $M$ railroads.\nYou are now at City $1$, with $10^{100}$ gold coins and $S$ silver coins in your pocket.\nThe $i$\\-th railroad connects City $U_i$ ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}
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