Language: C++

//実装が重そうな問題はある程度考えてから書く
//初期化を忘れずに（特に二分探索とか）
//コーナーケースを考えて（特に場合分けとか）
//不可解すぎるバグは配列外参照（配列の長さ）を検討
#include "bits/stdc++.h"
#define YES "YES"
#define Yes "Yes"
#define NO "NO"
#define No "No"
#define YESNO(x) OUT(three(x,YES,NO))
#define YesNo(x) OUT(three(x,Yes,No))
#define ECHO OUT(solve())
#define three(A,B,C) ((A)?(B):(C))
#define FOR(i,a,b)  for(LL i=(a);i< (LL)(b);i++)
#define EFOR(i,a,b) for(LL i=(a);i<=(LL)(b);i++)
#define RFOR(i,a,b) for(LL i=(a);i>=(LL)(b);i--)
#define REP(i,b) FOR(i,zero,b)
#define rep REP
#define EREP(i,b) EFOR(i,zero,b)
#define RREP(i,b) RFOR(i,b-1,zero)
#define ALL(c) c.begin(),c.end()
#define UNIQUE(c) sort(ALL(c));c.erase(unique(ALL(c)),c.end())
#define MAX(c) (*max_element(ALL(c)))
#define MIN(c) (*min_element(ALL(c)))
#define MP make_pair
#define FI first
#define SE second
#define SI(x) (LL(x.size()))
#define PB emplace_back
#define DEBUG(a) OUT(a)
#define DEBUG2(a,b) OUT2(a,b)
#define cat cout << __LINE__ << endl
#define OUT(a) cout << (a) << endl
#define OUT2(a,b) cout << (a) <<" "<<(b) << endl
#define int short
#define zero 0LL
#define all ALL
#define pb PB
using namespace std;
template<typename T> inline bool middle(T a, T b, T c) { return b <= a && a <= c; }
template<class T> inline bool MX(T &l, const T &r) { return l < r ? l = r, 1 : 0; }
template<class T> inline bool MN(T &l, const T &r) { return l > r ? l = r, 1 : 0; }
typedef long long LL;
typedef LL ll;
typedef double ld;
typedef LL ut;
const LL INF = 1LL << 60;
typedef vector<ut> VI;
typedef vector<VI> VII;
typedef pair<ut, ut> pr;
typedef pair<ut, pr> ppr;
typedef vector<pr> Vpr;
typedef vector<ppr> Vppr;
typedef priority_queue<ppr, Vppr ,greater<ppr> > PQ;
inline void outputVI(VI x) { REP(i, SI(x)) { cout << three(i, " ", "") << x[i]; }OUT(""); }
int dx[] = { 0,1,0,-1,1,1,-1,-1,0 }, dy[] = { 1,0,-1,0,1,-1,1,-1,0 };
const int SIZE1 =2e6 + 1000;
const int SIZE2 = 2010;
const int SIZE3 = 301;
const int SIZE = SIZE1;
const LL p = 7 + 1e9;const long double EPS = 1e-7;
ut N, M, K, X, L, Y,H,W,Q,D;
// ut A,B,C,D,E,F,G,H,I,J,O,P,Q,R,T,U;
VI edges[SIZE];
LL vals[SIZE], nums[SIZE], maps[SIZE2][SIZE2], answer = zero;
//LL A[SIZE], B[SIZE],I[SIZE];
LL A, B;
string s;
string revs;
LL DP[SIZE3][SIZE3][SIZE3];
bool checked[SIZE3][SIZE3][SIZE3];
LL solve2(int a,int b,int k) {
	if (a > b) return 0;
	if (a == b) return 1;
	if (checked[a][b][k]) return DP[a][b][k];
	checked[a][b][k] = true;

	if (s[a] == s[b]) {
		return DP[a][b][k] = solve2(a + 1, b - 1, k) + 2;
	}
	MX(DP[a][b][k], solve2(a + 1, b, k));
	MX(DP[a][b][k], solve2(a, b -1, k));
	if (k)
		MX(DP[a][b][k], solve2(a + 1, b -1, k - 1)+2);
	return DP[a][b][k];
	/*/
	if (max(a, b) >= s.size()) return 0;
	if (checked[a][b][k]) return DP[a][b][k];
	checked[a][b][k]=true;
	if (s[a] == revs[b]) {
		return DP[a][b][k] = solve2(a + 1, b + 1, k)+1;
	}
	MX(DP[a][b][k], solve2(a + 1, b, k));
	MX(DP[a][b][k], solve2(a , b+1, k));
	if(k)
		MX(DP[a][b][k], solve2(a + 1, b+1, k-1));
	return DP[a][b][k];
/*/
}
LL solve() {
	cin >> s;
	revs = s;
	reverse(ALL(revs));
	cin >> K;
	cout << solve2(0, (LL)s.size()-1, K) << endl;
	return 0;
}
signed main() {
	ios_base::sync_with_stdio(false);
	cout << fixed << setprecision(10);
	solve();
	//	cin >> N;
	return 0;
}

Compiler output:
a.cc:57:22: warning: overflow in conversion from 'double' to 'short int' changes value from '2.001e+6' to '32767' [-Woverflow]
   57 | const int SIZE1 =2e6 + 1000;
      |                  ~~~~^~~~~~
a.cc:64:10: error: size of array 'edges' exceeds maximum object size '9223372036854775807'
   64 | VI edges[SIZE];
      |          ^~~~
a.cc:65:9: error: size of array 'vals' exceeds maximum object size '9223372036854775807'
   65 | LL vals[SIZE], nums[SIZE], maps[SIZE2][SIZE2], answer = zero;
      |         ^~~~
a.cc:65:21: error: size of array 'nums' exceeds maximum object size '9223372036854775807'
   65 | LL vals[SIZE], nums[SIZE], maps[SIZE2][SIZE2], answer = zero;
      |                     ^~~~