Three-cushion billiards

On a frictionless plane, ball \(A\) moves with a velocity of \(v\) to collide elastically with two stopped balls \(B\) and \(C\) sequentially, as shown above. The masses of the three balls are the same as \(m.\) As indicated by the red arrows, the direction of ball \(A\)'s movement changes by an angle of \(45\)° each time there is a collision. What is the sum of the quantities of the impulses acting on ball \(A\) by balls \(B\) and \(C?\)

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