Given an array $c$, let $f(c)$ be the number of distinct elements in $c$. For example, $f([1,2,2])=2$ because there are two distinct elements in $[1,2,2]$: $1$ and $2$. Also, define $c[i,j]$ as the subarray$^{\text{∗}}$ of $c$ bounded by positions $i$ and $j$ (that is, the array $[c_i,c_{i+1},\ldots,c_j]$).

There is an array $a$ of size $n$. An array $b$ of $n$ elements is constructed such that $b_i=f(a[1,i])+f(a[2,i])+\ldots+f(a[i,i])$. You are given the array $b$. Find any possible $a$ with elements $1 \leq a_i \leq n$. It is guaranteed that at least one possible $a$ exists.

$^{\text{∗}}$An array $x$ is a subarray of an array $y$ if $x$ can be obtained from $y$ by the deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). The description of the test cases follows.

The first line of each test case contains an integer $n$ ($1 \leq n \leq 10^5$) – the number of elements in $a$ and $b$.

The second line of each test case contains $n$ integers $b_1,b_2,\ldots,b_n$ ($1 \leq b_i \leq 10^{18}$).

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

Output

For each test case, print any possible $a$ on a new line. The array $a$ should satisfy $1\leq a_i\leq n$.

For every test case, it is guaranteed at least one $a$ that satisfies the conditions exists.

Note

Let's verify our output for the second test case is correct:

• $b_1=f([2])=1$
• $b_2=f([2,3])+f([3])=2+1=3$
• $b_3=f([2,3,2])+f([3,2])+f([2])=2+2+1=5$