We choose an integer K (K > 0). Then we generate N (N > 0) integers one by one randomly, each of them is in range [0, K - 1], and the appearing probabilities of each interger is the same,they are all 1/K.
Can you tell us the expectation of the number of distinct integers in that N integers?

There is an integer T (1 <= T <= 200) in the first line, means there are T test cases in total.
For each test case, there are two integers K (1 <= K <= 1000), N (1 <= N <= 1000), which have the same meaning as above.

For each test case, you should print the result in one line. You should keep the first 5 digits after the decimal point.

Multi-University Contest Fina

没看出这是DP

看出来也不一定想得到

 1 #include <cstdio> 2 double dp[1005]; 3 int main() 4 { 5     int t; 6     scanf("%d", &t); 7     while (t--) 8      { 9         int m,n;10         scanf("%d %d", &m, &n);11         dp[1] = 1.0;12         for (int i = 2; i <= n; ++i)13             dp[i] = dp[i-1] + (m/1.0 - dp[i-1])/1.0/m;14         printf("%.5f\n", dp[n]);15     }16     return 0;17 }