You've got an array a, consisting of n integers. The array elements are indexed from 1 to n. Let's determine a two step operation like that:

  1. First we build by the array a an array s of partial sums, consisting of n elements. Element number i (1 ≤ i ≤ n) of array s equals <image>. The operation x mod y means that we take the remainder of the division of number x by number y. 
  2. Then we write the contents of the array s to the array a. Element number i (1 ≤ i ≤ n) of the array s becomes the i-th element of the array a (ai = si). 



You task is to find array a after exactly k described operations are applied.

Input

The first line contains two space-separated integers n and k (1 ≤ n ≤ 2000, 0 ≤ k ≤ 109). The next line contains n space-separated integers a1, a2, ..., an — elements of the array a (0 ≤ ai ≤ 109).

Output

Print n integers — elements of the array a after the operations are applied to it. Print the elements in the order of increasing of their indexes in the array a. Separate the printed numbers by spaces.

Examples

Input

3 1
1 2 3


Output

1 3 6


Input

5 0
3 14 15 92 6


Output

3 14 15 92 6
import java.io.BufferedReader;
import java.io.FileInputStream;
import java.io.InputStreamReader;
import java.util.HashMap;


public class E {
	
	public static long MOD = 1000000000L + 7L;
	
	static long inverse(long a, long b) {
		long x = 0, lastx = 1;
		long y = 1, lasty = 0;
		
		while(b != 0) {
			long quotient = a / b;
			long temp = a % b;
			a = b;
			b = temp;
			
			temp = x;
			x = lastx - quotient * x;
			lastx = temp;
			
			temp = y;
			y = lasty - quotient * y;
			lasty = y;
		}       
		if(lastx < 0) lastx += MOD;
	    return lastx;
	}
	
	public static void main(String[] args) throws Exception {
//		System.setIn(new FileInputStream("e.in"));
		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
		
		String[] parts = bf.readLine().trim().split("[ ]+");
		int N = Integer.parseInt(parts[0]);
		long K = Long.parseLong(parts[1]);
		
		long[] original = new long[N];
		parts = bf.readLine().trim().split("[ ]+");
		for(int i = 0; i < N; i++)
			original[i] = Long.parseLong(parts[i]);
		
		if(K == 0) {
			StringBuilder sb = new StringBuilder();
			for(int i = 0; i < N; i++) {
				if(i > 0) sb.append(" ");
				sb.append(original[i]);
			}
			
			System.out.println(sb);
			return;
		}
		/*
		 K--;
		
		long[] multipliers = new long[N];
		multipliers[0] = 1;
		
		for(int i = 1; i < N; i++)
			multipliers[i] = (((multipliers[i - 1] * (K + i)) % MOD) * inverse(i, MOD)) % MOD;

		StringBuilder sb = new StringBuilder();
		long result[] = new long[N];
		for(int i = 0; i < N; i++) {
			for(int j = i; j < N; j++) {
				result[j] += (multipliers[j - i] * original[i]) % MOD;
				result[j] %= MOD;
			}
		}
		
		for(int i = 0; i < N; i++) {			
			if(i > 0) sb.append(" ");
			sb.append(result[i]);
		}
		
		System.out.println(sb);
		 */
		K--;
		long[] multipliers = new long[N];
		multipliers[0] = 1;
		
		for(int i = 1; i < N; i++)
			multipliers[i] = (((multipliers[i - 1] * (K + i)) % MOD) * inverse(i, MOD)) % MOD;

		StringBuilder sb = new StringBuilder();
		long result[] = new long[N];
		for(int i = 0; i < N; i++) {
			for(int j = 0; j <= i; j++) {
				result[i] += (multipliers[i - j] * original[j]) % MOD;
				result[i] %= MOD;
			}
			
			if(i > 0) sb.append(" ");
			sb.append(result[i]);
		}
		
		System.out.println(sb);
	}

}
