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You're to have some drink. Each bottle of drink has \$n\$ extra parts than the drink(bottle, etc.) \$P_1, P_2, ..., P_n\$.
You can buy a bottle of drink using 1 dollar, \$a_1 P_1\$s, \$a_2 P_2\$s, ..., or \$a_n P_n\$s. When buying a bottle of drink, you also get one of each of \$P_1, P_2, ..., P_...