Hide and Seek 6

Interview

Time limit1sMemory limit512 MB

Summary

Given Subin's position S and the positions of N siblings, find the largest step size D such that repeated moves of +D or -D from S can reach every sibling.

Level: Medium4 of 10
Topics: Math, Number theory, Greedy, Implementation
Solved: No attempts yet

Problem

Subin is playing hide and seek with N younger siblings. Subin is currently at point S, and the siblings are at A1, A2, ..., AN.

Subin can move by walking. When Subin is at position X, walking moves her to X+D or X-D after 1 second. If Subin's position equals the position of a sibling, she has found that sibling.

She wants to choose the value of D so that she can find all the siblings. Find the maximum possible value of D.

Input

The first line gives N (1 ≤ N ≤ 105) and S (1 ≤ S ≤ 109). The second line gives the positions of the siblings Ai (1 ≤ Ai ≤ 109). All sibling positions are distinct and none equals Subin's position.

Output

Print the maximum possible value of D.

Examples3

Example 1
Input
```
3 3
1 7 11
```
Expected output
```
2
```
Example 2
Input
```
3 81
33 105 57
```
Expected output
```
24
```
Example 3
Input
```
1 1
1000000000
```
Expected output
```
999999999
```