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We need to make the length maximum. They have given that prime numbers can be distinct.
so we will start with least prime '2' and see that we use only this number. If we use distinct numbers we will get the length less than maximum.
x+3y<1000
Pick the numbers and make sure that the condition satisfies:
2^9=512 (X)
2^7 =128*3 = 348 (Y)
2^9+3*2^7 < 1000
Try next value:
2^10+3*2^7>1000 (condition is not satisfying)
=> 16 is the maximum length.
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