B'There are n students in a class working on group projects. The students will divide into groups (some students may be in groups alone), work on their independent pieces, and then discuss the results together. It takes the i-th student ai minutes to finish his/her independent piece. If students work at different paces, it can be frustrating for the faster students and stressful for the slower ones. In particular, the imbalance of a group is defined as the maximum ai in the group minus the minimum ai in the group. Note that a group containing a single student has an imbalance of 0. How many ways are there for the students to divide into groups so that the total imbalance of all groups is at most k? Two divisions are considered distinct if there exists a pair of students who work in the same group in one division but different groups in the other. The first line contains two space-separated integers n and k (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89200, 0 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89k xe2 x80 x89 xe2 x89 xa4 xe2 x80 x891000) -- the number of students and the maximum total imbalance allowed, respectively. The second line contains n space-separated integers ai (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89ai xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89500) -- the time it takes the i-th student to complete his/her independent piece of work. Print a single integer, the number of ways the students can form groups. As the answer may be large, print its value modulo 109 xe2 x80 x89+ xe2 x80 x897. In the first sample, we have three options: In the third sample, the total imbalance must be 0, so each student must work individually.'...