Cold Shower

Dohun lives alone and plans to take a shower over $n$ seconds.

Dohun's mysterious shower has a natural temperature change of $d_1, d_2, \ldots, d_n$ each time $1, 2, \ldots, n$ seconds pass. Dohun cannot predict this pattern, so he adjusts the shower based on the previous temperature.

Dohun's comfortable temperature $k$ is given.

Let $T_i$ be the shower temperature after $i$ seconds. The temperature $T_0$ at time $0$ is given.

Dohun adjusts the shower temperature as follows.

• If $T_i > k$ at time $i$, the water is too hot, so he sets $T_{i+1} = T_i + d_{i+1} - |T_i - k|$.
• If $T_i < k$ at time $i$, the water is too cold, so he sets $T_{i+1} = T_i + d_{i+1} + |T_i - k|$.
• If $T_i = k$ at time $i$, the water temperature is right, so he does not adjust it. That is, $T_{i+1} = T_i + d_{i+1}$.

The discomfort index is the sum of the differences between the shower temperature and the comfortable temperature at every second, starting from second 1. In other words, the discomfort index is $|T_1 - k| + |T_2 - k| + \cdots + |T_n - k|$.

Find the discomfort index that Dohun feels.

The first line contains three integers $n$, $k$, and $T_0$, separated by spaces.

The second line contains $n$ integers $d_1, d_2, \ldots, d_n$, separated by spaces.

Print Dohun's discomfort index.

$1 \le n \le 1\,000$

$0 \le k, T_0, d_i \le 100$