Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

A. Bear and Raspberry

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe bear decided to store some raspberry for the winter. He cunningly found out the price for a barrel of honey in kilos of raspberry for each of the following *n* days. According to the bear's data, on the *i*-th (1 ≤ *i* ≤ *n*) day, the price for one barrel of honey is going to is *x*_{i} kilos of raspberry.

Unfortunately, the bear has neither a honey barrel, nor the raspberry. At the same time, the bear's got a friend who is ready to lend him a barrel of honey for exactly one day for *c* kilograms of raspberry. That's why the bear came up with a smart plan. He wants to choose some day *d* (1 ≤ *d* < *n*), lent a barrel of honey and immediately (on day *d*) sell it according to a daily exchange rate. The next day (*d* + 1) the bear wants to buy a new barrel of honey according to a daily exchange rate (as he's got some raspberry left from selling the previous barrel) and immediately (on day *d* + 1) give his friend the borrowed barrel of honey as well as *c* kilograms of raspberry for renting the barrel.

The bear wants to execute his plan at most once and then hibernate. What maximum number of kilograms of raspberry can he earn? Note that if at some point of the plan the bear runs out of the raspberry, then he won't execute such a plan.

Input

The first line contains two space-separated integers, *n* and *c* (2 ≤ *n* ≤ 100, 0 ≤ *c* ≤ 100), — the number of days and the number of kilos of raspberry that the bear should give for borrowing the barrel.

The second line contains *n* space-separated integers *x*_{1}, *x*_{2}, ..., *x*_{n} (0 ≤ *x*_{i} ≤ 100), the price of a honey barrel on day *i*.

Output

Print a single integer — the answer to the problem.

Examples

Input

5 1

5 10 7 3 20

Output

3

Input

6 2

100 1 10 40 10 40

Output

97

Input

3 0

1 2 3

Output

0

Note

In the first sample the bear will lend a honey barrel at day 3 and then sell it for 7. Then the bear will buy a barrel for 3 and return it to the friend. So, the profit is (7 - 3 - 1) = 3.

In the second sample bear will lend a honey barrel at day 1 and then sell it for 100. Then the bear buy the barrel for 1 at the day 2. So, the profit is (100 - 1 - 2) = 97.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jan/20/2020 07:55:42 (e1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|