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.

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