In which direction and with what magnitude of acceleration a should the middle block be moved

In which direction and with what magnitude of acceleration a should the middle block be moved so that the load of mass m remains at rest?

We will use the kinematic connection formula:
a1 + a2 + 2 * a = 0;
Then, it turns out:
m1 * a1 = m1 * g – T;
m2 * a2 = m2 * g – T;
Now, we can assume that a1 = 0.
We get:
0 = m1 * g – T;
m2 * a2 = m2 * g – T;
0 + a2 + 2 * a = 0;
Let’s transform:
T = m1 * g;
m2 * a2 = m2 * g – m1 * g;
a = – a2 / 2;
Let’s find a:
a2 = g * (1 – m1 / m2);
a = – g * (1 – m1 / m2) / 2;
Then:
m1 = 2 * m2;
Suppose that a2 = 0, then as a result of similar calculations we get:
a = – g * (1 – m2 / m1) / 2;
a = – g * (1 – 1/2) / 2 = – g / 4;
Answer: if you move downward with an acceleration of g / 2; if you move up with an acceleration of -g / 4.