108. Self-numbers 2
time limit per test: 0.5
sec. In 1949 the Indian mathematician D.R. Kaprekar discovered a class of numbers called self-numbers. For any positive integer n, define d(n) to be n plus the sum of the digits of n. (The d stands for digitadition, a term coined by Kaprekar.) For example, d(75) = 75 + 7 + 5 = 87. Given any positive integer n as a starting point, you can construct the infinite increasing sequence of integers n, d(n), d(d(n)), d(d(d(n))), .... For example, if you start with 33, the next number is 33 + 3 + 3 = 39, the next is 39 + 3 + 9 = 51, the next is 51 + 5 + 1 = 57, and so you generate the sequence 33, 39, 51, 57, 69, 84, 96, 111, 114, 120, 123, 129, 141, ... The number n is called a generator of d(n). In the sequence above, 33 is a generator of 39, 39 is a generator of 51, 51 is a generator of 57, and so on. Some numbers have more than one generator: for example, 101 has two generators, 91 and 100. A number with no generators is a self-number. Let the a[i] will be i-th self-number. There are thirteen self-numbers a[1]..a[13] less than 100: 1, 3, 5, 7, 9, 20, 31, 42, 53, 64, 75, 86, and 97. (the first self-number is a[1]=1, the second is a[2] = 3, :, the thirteen is a[13]=97); Input Input contains integer numbers N, K, s_{1}...s_{k}. (1<=N<=10^{7}, 1<=K<=5000) delimited by spaces and line breaks. Output At first line you must output one number - the quantity of self-numbers in interval [1..N]. Second line must contain K numbers - a[s_{1}]..a[s_{k}], delimited by spaces. It`s a gaurantee, that all self-numbers a[s_{1}]..a[s_{k}] are in interval [1..N]. (for example if N = 100, s_{k} can be 1..13 and cannot be 14, because 14-th self-number a[14] = 108, 108 > 100) Sample Input 100 10 1 2 3 4 5 6 7 11 12 13 Sample Output 13 1 3 5 7 9 20 31 75 86 97 |