Digit Dynamic Programming Problem For Sum of Numbers

Question

I want to find the sum of all the positive integers in the range [1, N] with a given digit sum d. For example, if n = 100 and d = 7, the answer will be 7 + 16 + 25 + 34 + 43 + 52 + 61 + 70 = 308.

Following code can be used to count the numbers in the range [1, N] with a given digit sum d.

cnt[i][0][s] denotes count of suffixes that can be formed starting from index i, whose digits add up to s.

cnt[i][1][s] count of suffixes that can be formed starting from index i, whose digits add up to s such that the formed suffix is not greater than corresponding suffix in input string

#include <bits/stdc++.h>

using namespace std;

typedef long long int i64;

i64 cnt[20][2][200];

void digit_sum_dp(string ss) {
    int n = ss.size();

    for (int i = 0; i < 20; i++) {
        for (int j = 0; j < 2; j++) {
            for (int k = 0; k < 200; k++) {
                cnt[i][j][k] = 0;
            }
        }
    }

    cnt[n][0][0] = 1;
    cnt[n][1][0] = 1;
 
    for (int i = n - 1; i >= 0; i--) {
        for (int tight = 0; tight < 2; tight++) {
            for (int sum = 0; sum < 200; sum++) {
                if (tight) {
                    for (int d = 0; d <= ss[i] - '0'; d++) {
                        if (d == ss[i] - '0') {
                            cnt[i][1][sum] += cnt[i + 1][1][sum - d];
                        } else {
                            cnt[i][1][sum] += cnt[i + 1][0][sum - d];
                        }
                    }
                } else {
                    for (int d = 0; d < 10; d++) {
                        cnt[i][0][sum] += cnt[i + 1][0][sum - d];
                    }
                }
            }
        }
    }
    return cnt[0][1][d];
}

int main() {
    string str = "100";
    int d = 7;
    cout << digit_sum_dp(str, d) << "\n";
    return 0;
}

I have tried to extend the code to find out the sum of numbers instead of the count of numbers. Following is a code snippet.

cnt[i][1][sum] += cnt[i + 1][1][sum - d];
tot[i][1][sum] += (d * cnt[i + 1][1][sum - d] + tot[i + 1][1][sum - d] * pow(10, i));

I am getting incorrect results for some of the inputs. I shall be grateful if someone can help me.