B"Dima and Anya love playing different games. Now Dima has imagined a new game that he wants to play with Anya. Dima writes n pairs of integers on a piece of paper (li, xe2 x80 x89ri) (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89li xe2 x80 x89< xe2 x80 x89ri xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89p). Then players take turns. On his turn the player can do the following actions: The player who can't make a move loses. Of course, Dima wants Anya, who will move first, to win. That's why Dima should write out such n pairs of integers (li, xe2 x80 x89ri) (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89li xe2 x80 x89< xe2 x80 x89ri xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89p), that if both players play optimally well, the first one wins. Count the number of ways in which Dima can do it. Print the remainder after dividing the answer by number 1000000007 (109 xe2 x80 x89+ xe2 x80 x897). Two ways are considered distinct, if the ordered sequences of the written pairs are distinct. The first line contains two integers n, p (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n xe2 x80 x89 xe2 x89 xa4 xe2 x80 x891000, xe2 x80 x891 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89p xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89109). The numbers are separated by a single space. In a single line print the remainder after dividing the answer to the problem by number 1000000007 (109 xe2 x80 x89+ xe2 x80 x897)."...