Bessie has an array of $n$ integers $a_1, a_2, \ldots, a_n$. Bessie performs $m$ operations on the array. The $i$-th operation sets $a_{b_i} = a_{b_i} + c_i$.

Unfortunately, due to rising RAM costs, Bessie's computer has limited memory, and whenever any element of the array is greater than $h$, her computer crashes, and every element in the array is reset to its original value.

After all operations have been performed, output the array $a$.

Input

The first line of the input contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases.

The first line of each test case contains three integers $n, m, h$ ($1 \le n, m \le 2 \cdot 10^5$, $1 \leq h \leq 10^9$) — the length of array $a$, the number of operations performed, and the maximum value that Bessie's computer can store without crashing.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i \le h$) — the array $a$.

The next $m$ lines contain two integers $b_i, c_i$ ($1 \leq b_i \leq n$, $0 \leq c_i \leq 10^9$) — the operations that Bessie performs on the array.

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

Output

For each test case, output the array $a$ after all operations have been performed.

Note

For the first test case, the array $a$ is changed as follows:

• Before all operations, $a = [1, 2, 1]$.
• After the first operation, $a = [5, 2, 1]$.
• After the second operation, $a = [5, 6, 1]$, but since $6 \gt h$, the computer crashes, and $a = [1, 2, 1]$.
• After the third operation, $a = [1, 2, 4]$.
• After the fourth operation, $a = [1, 2, 4]$.

For the third test case, each operation causes the computer to crash, so $a = [1, 0, 0, 0]$.

Samples

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

1 2 4 
1 1 1 1 1 
1 0 0 0