You've got a non-decreasing sequence *x*<sub class="lower-index">1</sub>, *x*<sub class="lower-index">2</sub>, ..., *x*<sub class="lower-index">*n*</sub> (1 ≤ *x*<sub class="lower-index">1</sub> ≤ *x*<sub class="lower-index">2</sub> ≤ ... ≤ *x*<sub class="lower-index">*n*</sub> ≤ *q*). You've also got two integers *a* and *b* (*a* ≤ *b*; *a*·(*n* - 1) &lt; *q*).

Your task is to transform sequence *x*<sub class="lower-index">1</sub>, *x*<sub class="lower-index">2</sub>, ..., *x*<sub class="lower-index">*n*</sub> into some sequence *y*<sub class="lower-index">1</sub>, *y*<sub class="lower-index">2</sub>, ..., *y*<sub class="lower-index">*n*</sub> (1 ≤ *y*<sub class="lower-index">*i*</sub> ≤ *q*; *a* ≤ *y*<sub class="lower-index">*i* + 1</sub> - *y*<sub class="lower-index">*i*</sub> ≤ *b*). The transformation price is the following sum: <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/2932f339c0d0f43caa55ecad28d2426256d02ff5.png" style="max-width: 100.0%;max-height: 100.0%;"/>. Your task is to choose such sequence *y* that minimizes the described transformation price.
The first line contains four integers *n*, *q*, *a*, *b* (2 ≤ *n* ≤ 6000; 1 ≤ *q*, *a*, *b* ≤ 10<sup class="upper-index">9</sup>; *a*·(*n* - 1) &lt; *q*; *a* ≤ *b*).

The second line contains a non-decreasing integer sequence *x*<sub class="lower-index">1</sub>, *x*<sub class="lower-index">2</sub>, ..., *x*<sub class="lower-index">*n*</sub> (1 ≤ *x*<sub class="lower-index">1</sub> ≤ *x*<sub class="lower-index">2</sub> ≤ ... ≤ *x*<sub class="lower-index">*n*</sub> ≤ *q*).
print("_RANDOM_GUESS_1689258831.016191")# 1689258831.0162072