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E. Qpwoeirut and Vertices
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a connected undirected graph with $$$n$$$ vertices and $$$m$$$ edges. Vertices of the graph are numbered by integers from $$$1$$$ to $$$n$$$ and edges of the graph are numbered by integers from $$$1$$$ to $$$m$$$.

Your task is to answer $$$q$$$ queries, each consisting of two integers $$$l$$$ and $$$r$$$. The answer to each query is the smallest non-negative integer $$$k$$$ such that the following condition holds:

  • For all pairs of integers $$$(a, b)$$$ such that $$$l\le a\le b\le r$$$, vertices $$$a$$$ and $$$b$$$ are reachable from one another using only the first $$$k$$$ edges (that is, edges $$$1, 2, \ldots, k$$$).
Input

The first line contains a single integer $$$t$$$ ($$$1\le t\le 1000$$$) — the number of test cases.

The first line of each test case contains three integers $$$n$$$, $$$m$$$, and $$$q$$$ ($$$2\le n\le 10^5$$$, $$$1\le m, q\le 2\cdot 10^5$$$) — the number of vertices, edges, and queries respectively.

Each of the next $$$m$$$ lines contains two integers $$$u_i$$$ and $$$v_i$$$ ($$$1\le u_i, v_i\le n$$$) — ends of the $$$i$$$-th edge.

It is guaranteed that the graph is connected and there are no multiple edges or self-loops.

Each of the next $$$q$$$ lines contains two integers $$$l$$$ and $$$r$$$ ($$$1\le l\le r\le n$$$) — descriptions of the queries.

It is guaranteed that that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$, the sum of $$$m$$$ over all test cases does not exceed $$$2\cdot 10^5$$$, and the sum of $$$q$$$ over all test cases does not exceed $$$2\cdot 10^5$$$.

Output

For each test case, print $$$q$$$ integers — the answers to the queries.

Example
Input
3
2 1 2
1 2
1 1
1 2
5 5 5
1 2
1 3
2 4
3 4
3 5
1 4
3 4
2 2
2 5
3 5
3 2 1
1 3
2 3
1 3
Output
0 1 
3 3 0 5 5 
2
Note
Graph from the first test case. The integer near the edge is its number.

In the first test case, the graph contains $$$2$$$ vertices and a single edge connecting vertices $$$1$$$ and $$$2$$$.

In the first query, $$$l=1$$$ and $$$r=1$$$. It is possible to reach any vertex from itself, so the answer to this query is $$$0$$$.

In the second query, $$$l=1$$$ and $$$r=2$$$. Vertices $$$1$$$ and $$$2$$$ are reachable from one another using only the first edge, through the path $$$1 \longleftrightarrow 2$$$. It is impossible to reach vertex $$$2$$$ from vertex $$$1$$$ using only the first $$$0$$$ edges. So, the answer to this query is $$$1$$$.

Graph from the second test case. The integer near the edge is its number.

In the second test case, the graph contains $$$5$$$ vertices and $$$5$$$ edges.

In the first query, $$$l=1$$$ and $$$r=4$$$. It is enough to use the first $$$3$$$ edges to satisfy the condition from the statement:

  • Vertices $$$1$$$ and $$$2$$$ are reachable from one another through the path $$$1 \longleftrightarrow 2$$$ (edge $$$1$$$).
  • Vertices $$$1$$$ and $$$3$$$ are reachable from one another through the path $$$1 \longleftrightarrow 3$$$ (edge $$$2$$$).
  • Vertices $$$1$$$ and $$$4$$$ are reachable from one another through the path $$$1 \longleftrightarrow 2 \longleftrightarrow 4$$$ (edges $$$1$$$ and $$$3$$$).
  • Vertices $$$2$$$ and $$$3$$$ are reachable from one another through the path $$$2 \longleftrightarrow 1 \longleftrightarrow 3$$$ (edges $$$1$$$ and $$$2$$$).
  • Vertices $$$2$$$ and $$$4$$$ are reachable from one another through the path $$$2 \longleftrightarrow 4$$$ (edge $$$3$$$).
  • Vertices $$$3$$$ and $$$4$$$ are reachable from one another through the path $$$3 \longleftrightarrow 1 \longleftrightarrow 2 \longleftrightarrow 4$$$ (edges $$$2$$$, $$$1$$$, and $$$3$$$).

If we use less than $$$3$$$ of the first edges, then the condition won't be satisfied. For example, it is impossible to reach vertex $$$4$$$ from vertex $$$1$$$ using only the first $$$2$$$ edges. So, the answer to this query is $$$3$$$.

In the second query, $$$l=3$$$ and $$$r=4$$$. Vertices $$$3$$$ and $$$4$$$ are reachable from one another through the path $$$3 \longleftrightarrow 1 \longleftrightarrow 2 \longleftrightarrow 4$$$ (edges $$$2$$$, $$$1$$$, and $$$3$$$). If we use any fewer of the first edges, nodes $$$3$$$ and $$$4$$$ will not be reachable from one another.