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2459.   Almost the shortest route
Time Limit: 4.0 Seconds   Memory Limit: 65536K
Total Runs: 597   Accepted Runs: 134    Multiple test files
Case Time Limit: 2.0 Seconds

N cities (2 ≤ N ≤ 10 000) are connected by a network of M one-way roads (1 ≤ M < 100 000). It is known that these roads do not cross outside the cities. The numeration of the cities and the roads starts from 1. There is at most one road from any city to another one. The length of each road does not exceed 10 000.

The company for which you work sends you on a business trip from city 1 to city N on your personal car. The trip expenses will be compensated to you only if the distance you drive will differ from the shortest possible by no more than K (0 ≤ K ≤ 10 000).

The task is to determine on which roads you can drive to have the right to the compensation. That means the list of all roads that appear on at least one route from city 1 to city N where the length of the route does not exceed the length of the shortest route by more than K.


Input data consists of M+1 lines. The first line contains the numbers N, M, and K. Each next line describes one road and contains the initial city number, the final city number and the length of the road. All numbers are integers and separated from each other by one or more spaces.


Output data consists of several lines. The first line contains the integer L — the number of roads you can use. The following L lines contain the numbers of the roads in ascending order.

Example of input data

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

Example of output data


Source: Northeastern Europe 2003 Western Subregion
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