You are given an polynomial of x consisting of only addition marks, multiplication marks, brackets, single digit numbers, and of course the letter x. For example, a valid polynomial would be: (1+x)*(1+x*x+x+5)+1*x*x.
You are required to write the polynomial into it's minimal form by combining the equal terms.
For example, (1+x)*(1+x) would be written as x^2+2*x+1.
Also, (1+x)*(1+x*x+x+5)+1*x*x would be written as x^3+3*x^2+7*x+6.
The first line contains an integer T, meaning the number of the cases. 1 <= T <= 50.
For each test case, there will be one polynomial which it's length would be not larger than 1000.
It is guaranteed that every input polynomial is valid, and every number would be a single digit.
For each polynomial, output it's minimal form. If the polynomial's minimal form has n terms, output n space-separated integers.
You only have to output each term's corresponding constant (from highest to lowest). In case the constant gets too big, output the remainder of dividing the answer by 1000000007 (1e9 + 7).
4 1*(1+1*(1+1)) (1+x)*(1+x) x*((1+x)*(1+x*x+x+5)+1*x*x) (x*x*x*0+x*2)*x
3 1 2 1 1 3 7 6 0 2 0 0