M =: 1000000007
P =: M&|@^
T =: M|*
A =: {{{:p{{(>:a),d,M|c+d=.T/b,(1 2+n-+:a),(M-2)P~T/(a P 2),2 P 2*>:m['a b c'=.y}}x^:(<.-:x)1,,~2 P x*>:p=.x%~y-x}}

problem743 =: 1e8 A 1e16