P13008 【MX-X13-T3】"KDOI-12" Only by Losing Light Can You Escape Darkness

Given a non-negative integer $x$, you need to transform it into $y$ through a series of operations with the minimum cost. Each operation is defined as follows: * Choose an integer $0 \leq i \leq k$, and pay a cost of $a_i$ to either add or subtract $2^i$ from $x$. **Note: You do not need to ensure that $x$ remains non-negative during the operations.**

For each test case, output a single non-negative integer—the minimum cost required to transform $x$ into $y$.

For each test case, output a single non-negative integer—the minimum cost required to transform $x$ into $y$.

### **Sample Explanation** For the second test case in the sample input, the following two operations transform $x$ into $y$ with the minimum cost: 1. Choose $i=2$, perform $x \gets x + 2^2$, resulting in $x=6$ with a cost of $2$. 2. Choose $i=0$, perform $x \gets x - 2^0$, resulting in $x=5$ with an additional cost of $2$, totaling $4$. ### **Data Range** **This problem uses bundled testing.** | Subtask | Points | $T \leq$ | $x, y