Let m≥5 be an odd integer, and let D(m) denote the number of quadruples (a1,a2,a3,a4) of distinct integers with 1≤ai≤m for all i such that m divides a1+a2+a3+a4. There is a polynomial
q(x)=c3x3+c2x2+c1x+c0such that D(m)=q(m) for all odd integers m≥5. What is c1?(<spanclass=′latex−bold′>A</span>)−6(<spanclass=′latex−bold′>B</span>)−1(<spanclass=′latex−bold′>C</span>)4(<spanclass=′latex−bold′>D</span>)6(<spanclass=′latex−bold′>E</span>)11