Cowmpetency

Time limit2sMemory limit1024 MB

Summary

Fill the forgotten scores so the sequence is lexicographically smallest and each (a, h) pair makes cow h the first to beat cows 1 through a, or print -1.

Level: Medium6 of 10
Topics: Array, Greedy, Implementation
Solved: No attempts yet

Problem

Farmer John is hiring a new herd leader for his cows. To that end, he has interviewed $N$ ( $2 \leq N \leq 10^5$ ) cows for the position. After interviewing the $i$ th candidate, he assigned the candidate an integer "cowmpetency" score $c_i$ ranging from $1$ to $C$ inclusive ( $1 \leq C \leq 10^9$ ) that is correlated with their leadership abilities.

Because he has interviewed so many cows, Farmer John does not remember all of their cowmpetency scores. However, he does remember $Q$ ( $1 \leq Q < N$ ) pairs of numbers $(a_j, h_j)$ where cow $h_j$ was the first cow with a strictly greater cowmpetency score than cows $1$ through $a_j$ (so $1 \leq a_j < h_j \leq N$ ).

Farmer John now tells you the sequence $c_1, \dots, c_N$ (where $c_i = 0$ means that he has forgotten cow $i$ 's cowmpetency score) and the $Q$ pairs of $(a_j, h_j)$ . Help him determine the lexicographically smallest sequence of cowmpetency scores consistent with this information, or that no such sequence exists! A sequence of scores is lexicographically smaller than another if it assigns a smaller score to the first cow at which the two sequences differ.

Input

The first line contains $T$ , the number of independent test cases ( $1 \leq T \leq 20$ ). Each test case is described as follows:

A line containing $N$ , $Q$ , and $C$ .
A line containing the sequence $c_1, \dots, c_N$ ( $0 \leq c_i \leq C$ ).
$Q$ lines each containing a pair $(a_j, h_j)$ . All $a_j$ within a test case are distinct.

The sum of $N$ across all test cases does not exceed $3 \cdot 10^5$ .

Output

For each test case, output a single line containing the lexicographically smallest sequence of cowmpetency scores consistent with the information, or $-1$ if no such sequence exists.

Examples2

Example 1

Input

1
7 3 5
1 0 2 3 0 4 0
1 2
3 4
4 5

Expected output

1 2 2 3 4 4 1

Example 2

Input

5
7 6 10
0 0 0 0 0 0 0
1 2
2 3
3 4
4 5
5 6
6 7
8 4 9
0 0 0 0 1 6 0 6
1 3
6 7
4 7
2 3
2 1 1
0 0
1 2
10 4 10
1 2 0 2 1 5 8 6 0 3
4 7
1 2
5 7
3 7
10 2 8
1 0 0 0 0 5 7 0 0 0
4 6
6 9

Expected output

1 2 3 4 5 6 7
1 1 2 6 1 6 7 6
-1
1 2 5 2 1 5 8 6 1 3
-1