Saving Snuuk

AtCoder

IDsoundhound2018_summer_qual_d

Time2000ms

Memory256MB

Difficulty—

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: $n$ $m$ $s$ $t$ $u_1$ $v_1$ $a_1$ $b_1$ $:$ $u_m$ $v_m$ $a_m$ $b_m$ [samples]

Samples

Input #1

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.

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

Output #2

999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994

API Response (JSON)

{
  "problem": {
    "name": "Saving Snuuk",
    "description": {
      "content": "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 $",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "soundhound2018_summer_qual_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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 $...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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