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F. Cities Excursions
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

There are n cities in Berland. Some pairs of them are connected with m directed roads. One can use only these roads to move from one city to another. There are no roads that connect a city to itself. For each pair of cities (x, y) there is at most one road from x to y.

A path from city s to city t is a sequence of cities p 1, p 2, ... , p k, where p 1 = s, p k = t, and there is a road from city p i to city p i + 1 for each i from 1 to k - 1. The path can pass multiple times through each city except t. It can't pass through t more than once.

A path p from s to t is ideal if it is the lexicographically minimal such path. In other words, p is ideal path from s to t if for any other path q from s to t p i < q i, where i is the minimum integer such that p i ≠ q i.

There is a tourist agency in the country that offers q unusual excursions: the j-th excursion starts at city s j and ends in city t j.

For each pair s j, t j help the agency to study the ideal path from s j to t j. Note that it is possible that there is no ideal path from s j to t j. This is possible due to two reasons:

  • there is no path from s j to t j;
  • there are paths from s j to t j, but for every such path p there is another path q from s j to t j, such that p i > q i, where i is the minimum integer for which p i ≠ q i.

The agency would like to know for the ideal path from s j to t j the k j-th city in that path (on the way from s j to t j).

For each triple s j, t j, k j (1 ≤ j ≤ q) find if there is an ideal path from s j to t j and print the k j-th city in that path, if there is any.

Input

The first line contains three integers n, m and q (2 ≤ n ≤ 3000,0 ≤ m ≤ 3000, 1 ≤ q ≤ 4·105) — the number of cities, the number of roads and the number of excursions.

Each of the next m lines contains two integers x i and y i (1 ≤ x i, y i ≤ n, x i ≠ y i), denoting that the i-th road goes from city x i to city y i. All roads are one-directional. There can't be more than one road in each direction between two cities.

Each of the next q lines contains three integers s j, t j and k j (1 ≤ s j, t j ≤ n, s j ≠ t j, 1 ≤ k j ≤ 3000).

Output

In the j-th line print the city that is the k j-th in the ideal path from s j to t j. If there is no ideal path from s j to t j, or the integer k j is greater than the length of this path, print the string '-1' (without quotes) in the j-th line.

Example
Input
7 7 5
1 2
2 3
1 3
3 4
4 5
5 3
4 6
1 4 2
2 6 1
1 7 3
1 3 2
1 3 5
Output
2
-1
-1
2
-1