there n cell number 12dot n leave right you place robot cell initially the robot exactly k movesIn robot cell leave right provide do not bound in word robot cell cell i1 cell i1 long lie 1 n endpoint inclusive the cell order visit include cell robot place good patheach cell value a_i associate let c_0 c_1 dots c_k sequence cell good path order visit c_0 cell robot initially place c_1 cell robot formally c_i cell robot move then value path calculate a_c_0 a_c_1 dot a_c_kyour task calculate sum value possible good path since number large output modulo 109 7 two good path consider different start cell differ exist integer 1 k current cell robot exactly move different pathsyou process q update print update sum time each update change value exactly cell see input format sample inputoutput detail