Given that 0 ≤ A-B ≤ 1, 1 ≤ a + B ≤ 4, then when a-2b reaches the maximum, 8A + 2002b is equal to 0______ ．

Let m (a-b) + n (a + b) = a-2b, then (M + n) a + (- M + n) B = a-2b, comparing the coefficients of a and B, we can get m = 32, n = - 12; so a-2b = 32 (a-b) - 12 (a + b), then - 2 ≤ a-2b ≤ 1, so the maximum value of a-2b

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