{"raw_statement":[{"iden":"statement","content":"Vinh works for an ATM machine manufacturing company. The basic functionality of an ATM machine is cash withdrawal. When a user requests a cash withdrawal of W VND (Vietnamese Dong), the ATM has to dispense N money notes such that they sum up to W. For the next generation of ATM machine, Vinh is working on an algorithm to minimize the number N of money notes for each cash withdrawal transaction.\n\nYour task is to help Vinh to do his job given that the money notes come in the values of 1000, 2000, 3000, 5000, 1000 * 101, 2000 * 101, 3000 * 101, 5000 * 101, ..., 1000 * 10c, 2000 * 10c, 3000 * 10c, 5000 * 10c where c is a positive integer and Vinh has unlimited supply of money notes for each value. \n\nThe input file consists of several datasets. The first line of the input file contains the number of datasets which is a positive integer and is not greater than 1000. The following lines describe the datasets.\n\nFor each dataset, write in one line two space-separated integers N and S where S is the number of ways to dispense the fewest number N of money notes. In case there is no way to serve the cash withdrawal request, write out 0 in one line instead.\n\n"},{"iden":"input","content":"The input file consists of several datasets. The first line of the input file contains the number of datasets which is a positive integer and is not greater than 1000. The following lines describe the datasets.  The first line consists of one positive integer W (W ≤ 1018);  The second line consists of one positive integer c (c ≤ 15). "},{"iden":"output","content":"For each dataset, write in one line two space-separated integers N and S where S is the number of ways to dispense the fewest number N of money notes. In case there is no way to serve the cash withdrawal request, write out 0 in one line instead."},{"iden":"examples","content":"Input21000170001Output1 12 1"}],"translated_statement":null,"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ c \\in \\mathbb{Z}^+ $ be the exponent parameter.  \nLet $ V = \\{1000 \\cdot 10^k, 2000 \\cdot 10^k, 3000 \\cdot 10^k, 5000 \\cdot 10^k \\mid k \\in \\{0, 1, \\dots, c\\}\\} $ be the set of available banknote denominations.  \n\n**Given**  \nFor each dataset:  \n- $ W \\in \\mathbb{Z}^+ $: the requested withdrawal amount in VND.  \n- $ V $: denominations as defined above, with unlimited supply of each.  \n\n**Objective**  \nFor each dataset, find:  \n- $ N = \\min \\left\\{ \\sum_{v \\in V} x_v \\,\\middle|\\, \\sum_{v \\in V} x_v \\cdot v = W,\\, x_v \\in \\mathbb{Z}_{\\ge 0} \\right\\} $: the minimum number of notes.  \n- $ S $: the number of distinct combinations $ (x_v)_{v \\in V} $ achieving this minimum $ N $.  \n\nIf no such combination exists, output $ 0 $.  \n\n**Constraints**  \n- Number of datasets $ \\le 1000 $.  \n- $ W \\ge 1 $.  \n- $ c \\in \\mathbb{Z}^+ $ (implicitly defined by the denomination set).","simple_statement":"Given a target amount W and banknote denominations: 1000, 2000, 3000, 5000, and their multiples by powers of 10 up to 10^c, find the minimum number of notes N to make W, and count how many different ways to achieve this minimum N. If impossible, output 0.","has_page_source":false}