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
32 1 21 21 11 25 5 51 21 32 43 43 51 43 42 22 53 53 2 11 32 31 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.