## POLTOPOL - Polynomial f(x) to Polynomial h(x)

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Given polynomial of degree d, f(x)=c0+c1x+c2x2+c3x3+...+cdxd

For each polynomial f(x) there exists polynomial g(x) such that:

-> f(x)=g(x)-g(x-1) for each integer x

-> g(0)=0

(Note : degree of polynomial h(x) = degree of polynomial f(x))

### Input

The first line of input contain an integer T, T is number of test cases (0<T≤104)

Each test case consist of 2 lines:

- First line of the test case contain an integer d, d is degree of polynomial f(x) (0≤d≤18)

- Next line contains d+1 integers c0,c1,...,cd, separated by space, represent the coefficient of polynomial f(x) (-231<c0,c1,...,cd<231 and cd≠0)

### Output

For each test case, output the coefficient of polynomial h(x) separated by space. Each coefficient of polynomial h(x) is guaranteed to be an integer.

### Example

```Input:
5```
`0`
`13`
`1`
`-1 2`
`1`
`0 2`
`2`
`2 -5 9`
`3`
```23 9 21 104

Output:
13```
`0 1`
`1 1`
`1 2 3`
`31 41 59 26`

`---------------------------------------------------------------`
`Explanation for the first test case :`
`f(x)=13`
`g(x) that satisfy: g(x)-g(x-1)=f(x)=13 and g(0)=0 is: g(x)=13x`
`h(x)=g(x)/x so h(x)=13`
`output : 13`
`Explanation for the second test case :`
`f(x)=-1+2x`
`g(x) that satisfy: g(x)-g(x-1)=f(x)=-1+2x and g(0)=0 is: g(x)=x2`
`h(x)=g(x)/x so h(x)=x=0+1x`
`output : 0 1`
`Explanation for the third test case :`
`f(x)=0+2x`
`g(x) that satisfy: g(x)-g(x-1)=f(x)=2x and g(0)=0 is: g(x)=x+x2`
`h(x)=g(x)/x so h(x)=1+1x`
`output : 1 1`
`---------------------------------------------------------------`