you give tuple generator fk f_1k f_2k dot f_nk f_ik a_i cdot f_ik 1 b_i bmod p_i f0 x_1 x_2 dot x_n here x bmod y denote remainder x divide you all p_i primesOne fix sequence x_i y_i a_i tuple fk start index repeat tuple small index calculate maximum number different tuple fk k ge 0 produce generator x_i a_i b_i integer range 0 p_i 1 choose arbitrary the answer large print remainder gives divide 109 7