f = lambda: map(int, input().split())
n, m = f()
u = [0]
for i in range(n):
t = list(f())
k = t[0]
for i in range(1, k): t[i + 1] += t[i]
v = [t[k]] * (k + 1)
v[0] = t[0] = 0
for d in range(1, k):
v[k - d] -= min(t[j + d] - t[j] for j in range(k - d + 1))
p = [0] * (min(m, len(u) + len(v)) + 1)
for i, x in enumerate(u):
for j, y in enumerate(v, i):
if j > m: break
p[j] = max(p[j], x + y)
u = p
print(u[m])
#include <bits/stdc++.h>
using namespace std;
using i64 = long long;
int main() {
cin.tie(nullptr)->sync_with_stdio(false);
cout.setf(ios::fixed), cout.precision(8);
int n, m;
cin >> n >> m;
vector<vector<int>> a(n);
for (int i = 0; i < n; i++) {
int c;
cin >> c;
a[i].resize(c + 1);
a[i].assign(c + 1, 1E5);
a[i][0] = 0;
vector<vector<int>> b(c + 1, vector<int> (c + 1));
for (int j = 1; j <= c; j++) {
int x;
cin >> x;
a[i][0] += x;
for (int k = 1; k <= j; k++) {
b[j][k] = x + b[j - 1][k - 1];
a[i][c - k] = min(a[i][c - k], b[j][k]);
}
}
for (int j = 1; j <= c; j++) {
a[i][j] = a[i][0] - a[i][j];
}
a[i][c] = a[i][0];
a[i][0] = c;
}
vector<int> dp(m + 1);
for (int i = 0; i < n; i++) {
for (int j = m; j >= 0; j--) {
for (int k = 1; k <= min(j, a[i][0]); k++) {
dp[j] = max(dp[j], dp[j - k] + a[i][k]);
}
}
}
cout << dp[m];
return 0;
}
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