Problem: Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.

Submission attempts (in order):
#ifdef mmlang_source_11_lines

S = inputInt()

@memo(size=2005)
def func(x) -> int:
    if x<3:
        return 0
    ret = 1
    ret += func(x-(3:x-3+1)) mod 1e9+7
    return ret

print(func(S))

#endif

//#define NDEBUG



#include <deque>
#include <string>
#include <map>

#include <stack>
#include <algorithm>
#include <cstdlib>
#include <cstdio>
#include <cstring>

using namespace std;

typedef long long int64;typedef __int128 int128;const char*inputCLineOrWord(int mode){static char buf[2097152];static int bufLen=sizeof(buf);static int bufPos=sizeof(buf);static bool canReadFlag=true;static bool crFlag=false;static bool enterFlag=false;if(canReadFlag&&(enterFlag?bufLen<=bufPos:(int)sizeof(buf)<=bufPos+bufPos)){if(0<bufLen-bufPos){memmove(buf,buf+bufPos,bufLen-bufPos);bufLen-=bufPos;}else{bufLen=0;}char*result=fgets(buf+bufLen,sizeof(buf)-bufLen,stdin);canReadFlag=(result!=NULL);if(result!=NULL){int n=strlen(result);enterFlag=(n!=(int)sizeof(buf)-1-bufLen||(1<=bufLen+n&&buf[bufLen+n-1]=='\n'));bufLen+=n;}bufPos=0;}if(mode==0){int pos=bufPos;while(true){char c=buf[pos];if(c==32){buf[pos++]='\0';break;}else if(c==10){if(crFlag){crFlag=false;if(bufPos==pos){pos=++bufPos;continue;}}buf[pos++]='\0';break;}else if(c==13){crFlag=true;buf[pos++]='\0';break;}else if(c==0){break;}++pos;}const char*ret=buf+bufPos;bufPos=pos;while(true){char c=buf[bufPos];if(c==32||c==10||c==13){++bufPos;}else{break;}}return ret;}else if(mode==1){int pos=bufPos;while(true){char c=buf[pos];if(c==10){if(crFlag){crFlag=false;if(bufPos==pos){pos=++bufPos;continue;}}buf[pos++]='\0';break;}else if(c==13){crFlag=true;buf[pos++]='\0';break;}else if(c==0){break;}++pos;}const char*ret=buf+bufPos;bufPos=pos;if(crFlag){while(true){char c=buf[bufPos];if(c==13){++bufPos;crFlag=false;break;}else{break;}}}return ret;}else if(mode==2){return bufLen<=bufPos?NULL:buf+bufPos;}assert(false);return NULL;}const char*inputCWord(){return inputCLineOrWord(0);}int inputInt(){return atoi(inputCWord());}inline int mod(int x,int p){if(p<=x){do{x-=p;}while(p<=x);}else if(x<0){do{x+=p;}while(x<0);}return x;}void print_unit(bool val){printf("%s",val?"true":"false");}void print_unit(char val){printf("%c",val);}void print_unit(int val){printf("%d",val);}void print_unit(unsigned int val){printf("%u",val);}void print_unit(size_t val){printf("%zd",val);}void print_unit(const void*val){printf("%p",val);}void print_unit(long long val){printf("%lld",val);}void print_unit(__int128 val){char buf[128];int idx=128;buf[--idx]='\0';bool sign=false;if(val<0){sign=true;val=-val;}if(val==0){buf[--idx]='0';}else while(val){buf[--idx]='0'+(val % 10);val /=10;}if(sign){buf[--idx]='-';}printf("%s",buf+idx);}void print_unit(double val){printf("%g",val);}void print_unit(const char*val){printf("%s",val);}void print_unit(const std::string&val){printf("%s",val.c_str());}template<class T>void print_unit(const std::vector<T>&val){printf("vec(%d) {",(int)val.size());for(int i=0;i<(int)val.size();++i){fputc(' ',stdout);print_unit(val[i]);}printf(" }");}
#define _print0()
#define _print1(e)print_unit(e)
#define _print2(e1,e2)_print1(e1),fputc(' ',stdout),_print1(e2)
#define _print3(e1,e2,e3)_print2(e1,e2),fputc(' ',stdout),_print1(e3)
#define _print4(e1,e2,e3,e4)_print2(e1,e2),fputc(' ',stdout),_print2(e3,e4)
#define _print5(e1,e2,e3,e4,e5)_print3(e1,e2,e3),fputc(' ',stdout),_print2(e4,e5)
#define _print6(e1,e2,e3,e4,e5,e6)_print3(e1,e2,e3),fputc(' ',stdout),_print3(e4,e5,e6)
#define _print7(e1,e2,e3,e4,e5,e6,e7)_print4(e1,e2,e3,e4),fputc(' ',stdout),_print3(e5,e6,e7)
#define _print8(e1,e2,e3,e4,e5,e6,e7,e8)_print4(e1,e2,e3,e4),fputc(' ',stdout),_print4(e5,e6,e7,e8)
#define _print9(e1,e2,e3,e4,e5,e6,e7,e8,e9)_print5(e1,e2,e3,e4,e5),fputc(' ',stdout),_print4(e6,e7,e8,e9)
#define _print10(e1,e2,e3,e4,e5,e6,e7,e8,e9,e10)_print5(e1,e2,e3,e4,e5),fputc(' ',stdout),_print5(e6,e7,e8,e9,e10)
#define _GET_PRINT_MACRO_NAME(_1,_2,_3,_4,_5,_6,_7,_8,_9,_10,NAME,...)NAME
#define print(...)_GET_PRINT_MACRO_NAME(__VA_ARGS__,_print10,_print9,_print8,_print7,_print6,_print5,_print4,_print3,_print2,_print1,_print0)(__VA_ARGS__),fputc('\n',stdout)
#define print0(...)_GET_PRINT_MACRO_NAME(__VA_ARGS__,_print10,_print9,_print8,_print7,_print6,_print5,_print4,_print3,_print2,_print1,_print0)(__VA_ARGS__)

// generated code (by mmlang) :

int func(int x);

int S;

int func$origin(int x) {
    int ret;
    if(x < 3) {
        return 0;
    }
    ret = 1;
    for(int $e=x - 3 + 1, $1=3; $1<$e; ++$1) ret = mod((ret) + (func(x - ($1))), 1e9 + 7);
    return ret;
}
vector<int> func$memo;
int func(int x) {
    if(func$memo.empty()) {
        func$memo.resize(2005, (unsigned int)-1 >> 1);
    }
    auto & ref = func$memo[x];
    if(ref == (unsigned int)-1 >> 1) {
        ref = func$origin(x);
    }
    return ref;
}

int main() {
    S = inputInt();
    print(func(S));
    return 0;
}


S = int(input())

def memo(func):
  D = {}
  def ret(*args):
    if args not in D:
      D[args] = func(*args)
    return D[args]
  return ret

@memo
def func(x):
  if x<3:
    return 0
  ret = 1
  for i in range(3, x-3+1):
    ret = (ret + func(i)) % 1000000007
  return ret

print(func(S))


Verdicts: Runtime Error

Accepted