Perfect Sequence 怎么解答

Question

Problem Description
A sequence of integers is called a perfect sequence when all the partial sums a0, a0 + a1, a0 + a1 + a2, ..., a0 + a1 + ... + an are all positive.
Letⅴs consider a specific sequence , (ai = 1 or ai = (1-m), 1 ÷ i ÷ (m*n) ) , whose total sum is 1. Actually you can easily deduce that there are n occurrences of (1-m). So how many of these sequences are perfect sequences.

Input
Input contains several testcases.
For each test case, you will be given n, m (1 ÷ m, n ÷ 100000) in a single line.
Process to the end of the file.

Output
On each single line, output a number r mod 100000007, r is the number of perfect sequences (ai = 1 or ai = (1-m), 1 ÷ i ÷ (m*n) ) .

Sample Input
4 2
5 2
3 4

Sample Output
14
42
22

Answer 1

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# 读取数据
input <- readLines()

# 解析输入
n <- as.integer(input[1])
m <- as.integer(input[2])

# 初始化结果数组
result <- rep(0, length(m))

# 计算结果
for (i in 1:(n-1)) {
  for (j in 1:(m-1)) {
    result[i] += factorial(i+1)*factorial(j+1)*factorial((i+j)/2)
  }
}

# 输出结果
print(result)

# 定义阶乘函数
factorial <- function(n) {
  if (n == 0) return(1)
  else return(n * factorial(n - 1))
}

# 将结果模10^9+7进行处理
result <- apply(result, 1, function(x) x %% 100000007)

# 输出结果
print(result)