from right to left

class Solution {
    public String multiply(String num1, String num2) {
        int n = num1.length(), m = num2.length();

        int[] pos = new int[n + m];
        for (int i = n - 1; i >= 0; i--){
            for (int j = m - 1; j >= 0; j--){
                int mul = (num1.charAt(i) - '0') * (num2.charAt(j) - '0');
                int p1 = i + j, p2 = i + j + 1;
                int sum = mul + pos[p2];

                pos[p1] += sum / 10;
                pos[p2] = sum % 10;
            }
        }

        StringBuilder sb = new StringBuilder();
        for (int p : pos){
            if (sb.length() == 0 && p == 0) continue;
            sb.append(p);
        }

        return sb.length() == 0 ? "0" : sb.toString();
    }
}