разбиение на слагаемые по номеру

import java.io.File;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.Scanner;

public class dm3_task_21 {

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(new File("num2part.in"));
        PrintWriter printWr = new PrintWriter(new File("num2part.out"));
        //Scanner sc = new Scanner(System.in);
        int digit = sc.nextInt();
        int numOfPart = sc.nextInt();
        sc.close();
        int[] part = new int[digit];
        int[] tempSum = new int[digit];
        for (int i = 0; i < digit; i++) {
            part[i] = 1;
            tempSum[i] = i + 1;
        }
        int len = digit - 1;
        while (numOfPart > 0) {
            numOfPart--;
            do {
                if (tempSum[len] < digit) {
                    part[len]++;
                    tempSum[len]++;
                } else {
                    len--;
                    part[len]++;
                    tempSum[len]++;
                    int i = len + 1;
                    while (tempSum[i - 1] + part[len] <= digit) {
                        tempSum[i] = tempSum[i - 1] + part[len];
                        part[i] = part[len];
                        i++;
                    }
                    len = i - 1;
                }
            } while (tempSum[len] != digit);
        }
        for (int i = 0; i < len + 1; i++) {
            printWr.print(part[i]);
            //System.out.print(part[i]);
            if (i != len) {
                printWr.print("+");
                //System.out.print("+");
            }
        }
        printWr.close();
    }
}