Optimal Shopping II

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There are N junctions and M bidirectional roads, connecting these junctions. The junctions are numbered from 1 to N inclusive. For each road the time required to pass it is known.
There's a shop in every junction. Each shop contains some of K types of goods. In ith shop, the goods of the jth type cost A_{i,j} rubles.
Any item of the i^{th} type of goods weighs for W_{i} grams.
Initially, you are standing at the junction 1. You want to get to the junction N and buy exactly one unit of each of the goods so that your total budget does not exceed F rubles and the penalty is minimized (see next section for its details). Please note that buying goods take negligible time, so buying goods and switching roads can be considered instantaneous. Also, passing through junctions and roads multiple times is allowed. Also, note that you are also allowed to pass through junction N also, as long as in the end, you end up at this junction.
The penalty is defined as the sum of T_{i} * W_{i} over all types of goods, where T_{i} denotes the time between the moment of the purchase of the item of the goods of the i^{th} type and the finish moment. Intuitively, penalty is the cost you have to pay in carrying the goods.
Input
The first line contain four spaceseparated integer numbers N, M, K, F denoting the number of junctions, the number of roads, the number of types of goods and the budget respectively.
Each of the following K lines (say, the i^{th}) start with a pair of integer numbers P_{i} and W_{i} followed with P_{i} pairs of integers B_{i, j}, A_{i, j}, where B_{i, j} denotes a shop containing i^{th} good, the shop is located at junction B_{i, j} and the cost of i^{th} good at this junction will be A_{i, j}.
Each of the following M lines (say, the k^{th}) contains three spaceseparated integer numbers X_{k}, Y_{k}, Z_{k}, which denotes that there is a road whose two endpoint junctions are given by X_{k}, Y_{k} and the time required to pass this junction is given by Z_{k}.
Output
The first line of the output should contain an integer number D, denoting the number of commands.
The following line should contain D integer numbers, denoting the commands in the following format: Let the number outputted in some command is d.
 If d is positive, then it represents a move from the current junction to the adjacent junction numbered d.
 If d is negative, that it represents buying of the goods of type d in the current shop.
In the beginning, the current junction is always the first junction.
You will get a wrong answer verdict when:
 You try to move to the junction that is not adjacent to the current one.
 You don't finish at the junction N.
 You spend more than F rubles.
 You try to buy some goods in some shop where they're unavailable.
 You try to buy goods of same type twice or some.
 You don't buy all the goods by the time you finish.
 The number of commands exceeds 2000000.
Constraints
In order to ensure that the answer will always exist, the value of the sum of the minimal costs over all goods will not exceed F.
 It is possible to get from any junction to any other junction via the given roads.
 1 ≤ Z_{k} ≤ 10^{4}
 1 ≤ W_{i} ≤ 10^{4}
 1 ≤ F ≤ 10^{7}
 A shop can contain at most one good of a particular type, Hence for each junction i, B_{i, j}'s will be distinct.
Group 1:
 40 ≤ N ≤ 50
 80 ≤ M ≤ 100
 20 ≤ K ≤ 40
 10 ≤ A_{i, j} ≤ 30
Group 2:
 40 ≤ N ≤ 50
 80 ≤ M ≤ 100
 20 ≤ K ≤ 40
 10000 ≤ A_{i, j} ≤ 50000
Group 3:
 900 ≤ N ≤ 1000
 1000 ≤ M ≤ 10000
 100 ≤ K ≤ 500
 10 ≤ A_{i, j} ≤ 30
Group 4:
 900 ≤ N ≤ 1000
 1000 ≤ M ≤ 10000
 100 ≤ K ≤ 500
 10000 ≤ A_{i, j} ≤ 50000
Test data generation
Each of the four groups will contain five test cases. During the contest, you will only see the score on the set of four test cases  one from each group.
The junctionroad network structure will be random. The values of N, M, K will be picked from the given intervals randomly and independently.
For the distribution of the goods between shops, there will be picked a nonrandom interval [L; R], which is common for all goods within a test case. Each of the goods will go to P random shops, where P is picked randomly from the segment [L; R].
For each of the goods, the weight is picked randomly from the segment [1; 10^{4}].
Then, the sum S of minimal costs over all goods is calculated. The value of F will be equal to S multiplied by some random number within range [1.0; 1.1] (and rounded).
Scoring
Your score for a single test case will be calculated as a square root of the value of the penalty function, described in the statement.
Your score for the problem will be calculated as a sum of individual scores for each test case.
Example
Input: 4 6 2 28 3 50 2 13 4 17 3 15 2 91 3 19 2 15 2 1 34 1 3 46 3 4 18 1 4 54 2 4 90 3 2 38 Output: 5 2 1 2 3 4
Explanation
Input
There are 4 junctions, 6 roads and 2 types of goods. The total budget is 28.
The goods of the first type does weigh 50 and are sold in the shops at the junctions 2, 4, 3 with costs 13, 17, 15 respectively.
The goods of the second type does weigh 91 and are sold in the junctions 3, 2 with costs 19, 15 respectively.
Output
Let's perform the outputted commands:
 Command 2 means to move to junction 2. There is such a road, so the command is correct.
 Command 1 means to buy goods of the type 1. So we buy goods of the type 1, and spend 13 rubles.
 Command 2 means to buy goods of the type 2. So we buy goods of the type 2 and spend 15 burles. Now we've spent 28 burles in total, which is OK, since we didn't exceed the budget of 28 burles.
 Command 3 means to move to the third junction. Meanwhile, the penalty becomes equal to (50 + 91) * 38 = 5358.
 Command 4 means to move to the fourth junction. The penalty function becomes equal to (50 + 91) * (38 + 18) = 7896. We can finish now, since all goods are bought and we've reached the final junction.
Author:  xcwgf666 
Tester:  kevinsogo 
Editorial  http://discuss.codechef.com/problems/SHOP2 
Tags  challenge, may16, travelsalesman, xcwgf666 
Date Added:  29032016 
Time Limit:  5 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, SCM chicken, PYP3, CLOJ, FS 
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