On four color monochromatic sets with nondecreasing diameter

Let m and r be positive integers. Define f(m,r) to be the least positive integer N such that for every coloring of the integers 1,…,N with r colors there exist monochromatic subsets B1 and B2 (not necessarily of the same color), each having m elements, such that (a) max(B1)-min(B1)⩽max(B2)-min(B2), and (b) max(B1)