A shop sells bottles with this capacity: $1L, 2L, 3L,..., 1996L$, the prices of bottles satifies this $2$ conditions: $1$. Two bottles have the same price, if and only if, your capacities satifies $m - n = 1000$ $2$. The price of bottle $m$($1001>m>0$) is $1996 - m$ dollars. Find all pair(s) $m$ and $n$ such that: a) $m + n = 1000$ b) the cost is smallest possible!!! c) with the pair, the shop can measure $k$ liters, with $0<k<1996$(for all $k$ integer) Note: The operations to measure are: i) To fill or empty any one of two bottles ii)Pass water of a bottle for other bottle We can measure $k$ liters when the capacity of one bottle plus the capacity of other bottle is equal to $k$