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 OCaml (4.10.0) (judge verdict: Accepted)

open Core
open Stdio

let read_line () = In_channel.(input_line_exn stdin)

let money_inf = 50 * 50
let dist_inf = Int64.(10L ** 15L)
type edge_t = { cod : int; unchin : int; jikan : Int64.t }

let [n;m;s] = read_line () |> String.split ~on:' ' |> List.map ~f:Int.of_string
let s = min money_inf s

let edges = Array.create ~len:n []

let () =
    for i = 1 to m do
        let [u; v; un; ji] = read_line () |> String.split ~on:' ' in
        let u = Int.of_string u - 1 in
        let v = Int.of_string v - 1 in
        let un = Int.of_string un in
        let ji = Int64.of_string ji in
        edges.(u) <- { cod = v; unchin = un; jikan = ji } :: edges.(u);
        edges.(v) <- { cod = u; unchin = un; jikan = ji } :: edges.(v)
    done

let maisu_jikan_s = Array.init n ~f:(fun _ ->
    let x,y = read_line () |> String.lsplit2_exn ~on:' ' in
    let x = min money_inf (Int.of_string x) in
    let y = Int64.of_string y in
    (x,y))

let used = Array.make_matrix ~dimx:n ~dimy:(money_inf+1) false
let res = Array.make_matrix ~dimx:n ~dimy:(money_inf+1) dist_inf

let rec dijk mins = match Set.min_elt mins with
    | None -> ()
    | Some ((dist, v, money) as tup) ->
        let mins = Set.remove mins tup in
        if used.(v).(money) then dijk mins else begin
        used.(v).(money) <- true;
        res.(v).(money) <- Int64.min res.(v).(money) dist;
        (* printf "%Ld (%d, %d)\n" res.(v).(money) v money; *)
        (* 銀貨に交換 *)
        let mins = let money = money + fst maisu_jikan_s.(v) in
            let dist = Int64.(dist + snd maisu_jikan_s.(v)) in
            if money <= money_inf && not used.(v).(money) (* && Int64.(dist < res.(v).(money)) *)
            then Set.add mins (dist, v, money) 
            else mins in
        (* 別の都市に移動 *)
        let mins = List.fold edges.(v) ~init:mins ~f:(fun mins ch ->
            let money = money - ch.unchin in
            let dist = Int64.(dist + ch.jikan) in
            let v = ch.cod in
            if money >= 0 && not used.(v).(money) (* && Int64.(dist < res.(v).(money)) *)
            then Set.add mins (dist, v, money)
            else mins) in
        dijk mins
        end

module DijkData : (Comparator.S with type t = int64 * int * int) = struct
    type t = int64 * int * int
    include Comparator.Make (struct
        type t = int64 * int * int
        let compare = Tuple3.compare ~cmp1:Int64.compare ~cmp2:compare ~cmp3:compare
        let sexp_of_t = Tuple3.sexp_of_t Int64.sexp_of_t Int.sexp_of_t Int.sexp_of_t
    end)
end

let () = dijk (Set.singleton (module DijkData) (0L, 0, s));
(* let () = dijk (Map.singleton (module Int64) 0L (0, s)); *)
    for v = 1 to n - 1 do
        printf "%Ld\n" @@ Option.value_exn (Array.min_elt res.(v) ~compare:Int64.compare)
    done