Pro.ID22621 TitleSum of powers Title链接http://10.20.2.8/oj/exercise/problem?problem_id=22621 AC0 Submit0 Ratio- 时间&空间限制描述A young schoolboy would like to calculate the sum
for some fixed natural k and different natural n. He observed that calculating ik for all i ( 1 <= i <= n ) and summing up results is a too slow way to do it, because the number of required arithmetical operations increases as n increases. Fortunately, there is another method which takes only a constant number of operations regardless of n. It is possible to show that the sum Sk(n) is equal to some polynomial of degree k+1 in the variable n with rational coefficients, i.e.,
for some integer numbers M, ak+1, ak, ... , a1, a0. We require that integer M be positive and as small as possible. Under this condition the entire set of such numbers (i.e. M, ak+1, ak, ... , a1, a0) will be unique for the given k. You have to write a program to find such set of coefficients to help the schoolboy make his calculations quicker. 输入The input file contains a single integer k ( 1 <= k <= 20 ). 输出Description A young schoolboy would like to calculate the sum
for some fixed natural k and different natural n. He observed that calculating ik for all i ( 1 <= i <= n ) and summing up results is a too slow way to do it, because the number of required arithmetical operations increases as n increases. Fortunately, there is another method which takes only a constant number of operations regardless of n. It is possible to show that the sum Sk(n) is equal to some polynomial of degree k+1 in the variable n with rational coefficients, i.e.,
for some integer numbers M, ak+1, ak, ... , a1, a0. We require that integer M be positive and as small as possible. Under this condition the entire set of such numbers (i.e. M, ak+1, ak, ... , a1, a0) will be unique for the given k. You have to write a program to find such set of coefficients to help the schoolboy make his calculations quicker. Input The input file contains a single integer k ( 1 <= k <= 20 ). Output Write integer numbers M, ak+1, ak, ... , a1, a0 to the output file in the given order. Numbers should be separated by one or more spaces. Remember that you should write the answer with the smallest positive M possible. Sample Input 2Sample Output 6 2 3 1 0Source 样例输入2样例输出6 2 3 1 0作者 |
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