Further Mechancis Impulse question

A particle P, of mass 0.5 kg, is moving with velocity (4i + 4j) ms-1 when it receives an impulse I of magnitude 2.5 Ns. As a result of the impulse, the direction of motion of P is deflected through an angle of 45°.
Given that I = (λi + μj) Ns, find all the possible pairs of values of λ and μ.

How do I start with this question. The mark scheme uses a diagram with vector 2i + 2j, but I dont' get why that's used instead of 4i +4j

An impulse is (constant) force times time and it equals the change in momentum as
v-u = at
or
mv - mu = mat
and f=ma.

I have the formula, I'm just not sure where to go with it

A sketch helps so mark on either the initial momentum or the initial velocity and how might the impulse (force) be appllied to turn it through 45 degrees? You say youve got the mark scheme, so which part of that do/dont you understand.

My diagram looks like the mark scheme, only with 4i + 4j instead of 2i + 2j, It's where the 2i + 2j came from that I don't get

My diagram looks like the mark scheme, only with 4i + 4j instead of 2i + 2j, It's where the 2i + 2j came from that I don't get
The MS is page 6 of this: https://www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Fpmt.physicsandmathstutor.com%2Fdownload%2FMaths%2FA-level%2FFurther%2FMechanics%2FEdexcel%2FFM1%2FTopic-Qs%2FSet-A%2FCh.1%2520Momentum%2520and%2520Impulse.pdf