Manipulating the Balance Sheet

The balance sheet must satisfy

$$\text{assets}=\text{liabilities}+\text{equity}.$$

Let $A$ be the sum of undamaged asset amounts, and $B$ the sum of undamaged liability and equity amounts. Let $c_A$ and $c_R$ count damaged accounts on the asset side and on the other side, respectively.

• If $c_A>0$ and $c_R>0$, unknown amounts appear on both sides, so the restoration cannot be uniquely determined.
• If both liability and equity accounts are damaged, the type of the consolidated account is not unique; restoration is impossible.
• If , the original accounts are valid exactly when . In that case print them unchanged.

If the computed amount is negative, restoration is impossible. Otherwise, print every undamaged account in input order, followed by the consolidated OTHER account with that type and amount. Print it even if the amount is zero.

Each input amount is at most $10^9$, and there are at most $100\,000$ accounts, so the absolute value of every sum and recovered amount is at most $10^{14}$. Use a signed 64-bit integer.

Reading and printing the accounts takes $O(N)$ time and $O(N)$ space.