#include<bits/stdc++.h>
#define ll long long
using namespace std;

const int N = 3000 + 500;
int n, k, p[N], w[N][11];
ll f[N][11], summ;

int main() {
    scanf("%d %d", &n, &k); int sum = 0;
    memset(f, 0x80, sizeof(f));
    f[0][0] = 0;
    for (int i = 1; i <= n; i++) {
        scanf("%d", &p[i]); sum += p[i];
        for (int j = 1; j <= p[i]; j++) scanf("%d", &w[i][j]); summ += w[i][p[i]];
        for (int S = k; S >= 0; S--) {
            if (S >= p[i]) {
                f[S][0] = max(f[S][0], f[S - p[i]][0] + w[i][p[i]]);
                f[S][1] = max(f[S][1], f[S - p[i]][1] + w[i][p[i]]);
            }
            for (int j = 1; j <= p[i]; j++) {
                if (S - j < 0) break;
                f[S][1] = max(f[S][1], f[S - j][0] + w[i][j]);
            }
        }
    }
    if (sum < k) printf("%lld\n", summ);
        else printf("%lld\n", max(f[k][0], f[k][1]));

    return 0;
}