Wtd's army attacks wtc’s castle several times. However, wtc always wins these wars. Then, wtd wants to know the combat values of among different soldiers.

The
total combat values of soldiers in this planet is defined as addition among two
polynomials. Wtd asks you for help as he is not good at
math. Each time, wtd will give you the (**coefficient, exponent)** pairs
(These pairs will be given by in ascending order of exponent) of two polynomials. For
example, will be given as (1 0), (2 1), (3 2). You return the **polynomial
after addition to him**. Since the soldiers may be injured in the war, so the
coefficients could be negative values.

Note that, to help army master to understand:

**Please
pay attention to the special cases, e.g., the result is 0, the sum of compact
values is 0 or 1 at level i. We follow all these definitions and notations in
Math.**