문제

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 remembers $Q$ ($1 \leq Q < N$) 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 sequence of scores if it assigns a smaller score to the first cow at which the two sequences differ.

Each input contains $T$ $(1 \leq T \leq 20)$ independent test cases. The sum of $N$ across all test cases is guaranteed to not exceed $3 \cdot 10^5$.

입력

The first line contains $T$, the number of independent test cases. Each test case is described as follows: First, a line containing $N$, $Q$, and $C$.Next, a line containing the sequence $c_1, \dots, c_N$ $(0 \leq c_i \leq C)$.Finally, $Q$ lines each containing a pair $(a_j, h_j)$. It is guaranteed that all $a_j$ within a test case are distinct.

출력

For each test case, output a single line containing the lexicographically smallest sequence of cowmpetency scores consistent with what Farmer John remembers, or $-1$ if such a sequence does not exist.

예제 입력 1

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

예제 출력 1

1 2 2 3 4 4 1

예제 입력 2

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

예제 출력 2

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

점수

Input 3 satisfies $N \leq 10$ and $Q, C \leq 4$.Inputs 4-8 satisfy $N \leq 1000$.Inputs 9-12 satisfy no additional constraints.