Two carts, A and B, move along a horizontal frictionless track in the +x-direction. Cart A has mass m and Cart B has mass 2m, and both carts have the same initial linear momentum of magnitude p_0. A constant braking force of magnitude F_0 is applied in the -x-direction to each cart until it comes to rest. Which of the following correctly pairs the relationship between their initial kinetic energies, K_A and K_B, with the relationship between the time intervals, \(\Delta t_A\) and \(\Delta t_B\), required to bring each cart to rest?