Given a sequence of ~n~ integers ~A[1], A[2], \dots, A[n]~ and a positive integer ~M~, count the number of pairs ~(i, j)~ that satisfy the following two conditions:

• ~i < j~, and
• ~A[i] + A[j] \le M~.

Input Specification

The first line contains integer ~n\ ( 2 \le n \le 10^5 )~ and ~M\ ( 0 \le M \le 10^9 )~, separated by a space.
The second line contains ~n~ integers, which denotes ~A[1], A[2], \dots , A[n]\ (0 \le A[i] \le 10^9)~.
In 50% of the test cases, ~n \le 1\,000~.

Output Specification

The output contains an integer, which denotes the number of pairs that satisfies the two conditions. If the output is smaller than ~10^9+7~, please keep it as is. Otherwise, output the number mod ~10^9+7~.

Sample Input 1

5 6
1 2 3 4 5

Sample Output 1

6

Explanation for Sample Output 1

Among the pairs, ~(1, 2)~, ~(1, 3)~, ~(1, 4)~, ~(1, 5)~, ~(2, 3)~, ~(2, 4)~ satisfy the conditions.

Sample Input 2

5 12
3 6 8 2 8

Sample Output 2

7

Explanation for Sample Output 2

~(1, 2)~, ~(1, 3)~, ~(1, 4)~, ~(1, 5)~, ~(2, 4)~, ~(3, 4)~, ~(4, 5)~ satisfy the conditions.