Problem:
Score : 800 points

Problem Statement

Snuke has a string x of length N.
Initially, every character in x is 0.

Snuke can do the following two operations any number of times in any order:

Choose A consecutive characters in x and replace each of them with 0.

Choose B consecutive characters in x and replace each of them with 1.

Find the number of different strings that x can be after Snuke finishes doing operations.
This count can be enormous, so compute it modulo (10^9+7).

Constraints

1 \leq N \leq 5000

1 \leq A,B \leq N

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N A B

Output

Print the number of different strings that x can be after Snuke finishes doing operations, modulo (10^9+7).

Sample Input 1

4 2 3

Sample Output 1

11

For example, x can be 0011 or 1111 in the end, but cannot be 0110.

Sample Input 2

10 7 2

Sample Output 2

533

Sample Input 3

1000 100 10

Sample Output 3

828178524

Solution in C (GCC 9.2.1) (judge verdict: Accepted)

//set many funcs template
//Ver.20190820
#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<stdbool.h>
#include<time.h>
#include<assert.h>
#define inf 1072114514
#define llinf 4154118101919364364
#define mod 1000000007
#define pi 3.1415926535897932384

int max(int a,int b){if(a>b){return a;}return b;}
int min(int a,int b){if(a<b){return a;}return b;}
int zt(int a,int b){return max(a,b)-min(a,b);}
int round(int a,int b){if((a%b)*2 >= b){return (a/b)+1;}return a/b;}
int ceil(int a,int b){if(a%b==0){return a/b;}return (a/b)+1;}
int gcd(int a,int b){int c;while(b!=0){c=a%b;a=b;b=c;}return a;}
int lcm(int a,int b){int c=gcd(a,b);a/=c;return a*b;}
int nCr(int a,int b){int i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
int nHr(int a,int b){return nCr(a+b-1,b);}
int fact(int a){int i,r=1;for(i=1;i<=a;i++){r*=i;}return r;}
int pow(int a,int b){int i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}
int dsum(int x){int r=0;while(x){r+=(x%10);x/=10;}return r;}
int dsumb(int x,int b){int r=0;while(x){r+=(x%b);x/=b;}return r;}
int sankaku(int x){return ((1+x)*x)/2;}
void swap(int *a,int *b){int c;c=(*a);(*a)=(*b);(*b)=c;}
long long llmax(long long a,long long b){if(a>b){return a;}return b;}
long long llmin(long long a,long long b){if(a<b){return a;}return b;}
long long llzt(long long a,long long b){return llmax(a,b)-llmin(a,b);}
long long llround(long long a,long long b){if((a%b)*2 >= b){return (a/b)+1;}return a/b;}
long long llceil(long long a,long long b){if(a%b==0){return a/b;}return (a/b)+1;}
long long llgcd(long long a,long long b){long long c;while(b!=0){c=a%b;a=b;b=c;}return a;}
long long lllcm(long long a,long long b){long long c=llgcd(a,b);a/=c;return a*b;}
long long llnCr(long long a,long long b){long long i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
long long llnHr(long long a,long long b){return llnCr(a+b-1,b);}
long long llfact(long long a){long long i,r=1;for(i=1;i<=a;i++){r*=i;}return r;}
long long llpow(long long a,long long b){long long i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}
long long lldsum(long long x){long long r=0;while(x){r+=(x%10);x/=10;}return r;}
long long lldsumb(long long x,long long b){long long r=0;while(x){r+=(x%b);x/=b;}return r;}
long long llsankaku(long long x){return ((1+x)*x)/2;}
void llswap(long long *a,long long *b){long long c;c=(*a);(*a)=(*b);(*b)=c;}
double dbmax(double a,double b){if(a>b){return a;}return b;}
double dbmin(double a,double b){if(a<b){return a;}return b;}
double dbzt(double a,double b){return dbmax(a,b)-dbmin(a,b);}
void dbswap(double *a,double *b){double c;c=(*a);(*a)=(*b);(*b)=c;}
void chswap(char *a,char *b){char c;c=(*a);(*a)=(*b);(*b)=c;}
int sortfncsj(const void *a,const void *b){if(*(int *)a>*(int *)b){return 1;}if(*(int *)a==*(int *)b){return 0;}return -1;}
int sortfnckj(const void *a,const void *b){if(*(int *)a<*(int *)b){return 1;}if(*(int *)a==*(int *)b){return 0;}return -1;}
int llsortfncsj(const void *a,const void *b){if(*(long long *)a>*(long long *)b){return 1;}if(*(long long *)a==*(long long *)b){return 0;}return -1;}
int llsortfnckj(const void *a,const void *b){if(*(long long *)a<*(long long *)b){return 1;}if(*(long long *)a==*(long long *)b){return 0;}return -1;}
int dbsortfncsj(const void *a,const void *b){if(*(double *)a>*(double *)b){return 1;}if(*(double *)a==*(double *)b){return 0;}return -1;}
int dbsortfnckj(const void *a,const void *b){if(*(double *)a<*(double *)b){return 1;}if(*(double *)a==*(double *)b){return 0;}return -1;}
int strsortfncsj(const void *a,const void *b){return strcmp((char *)a,(char *)b);}
int strsortfnckj(const void *a,const void *b){return strcmp((char *)b,(char *)a);}
int chsortfncsj(const void *a,const void *b){if(*(char *)a>*(char *)b){return 1;}if(*(char *)a==*(char *)b){return 0;}return -1;}
int chsortfnckj(const void *a,const void *b){if(*(char *)a<*(char *)b){return 1;}if(*(char *)a==*(char *)b){return 0;}return -1;}

long long power(long long a,long long b){
  long long x=1,y=a;
  while(b>0){
    if(b&1ll){
      x=(x*y)%mod;
    }
    y=(y*y)%mod;
    b>>=1;
  }
  return x%mod;
}

long long modular_inverse(long long n){
  return power(n,mod-2);
}

int main(void){
  long long i,j,n,m,k,a,b,c,h,w,r=0,l,t,pt;
  long long dp[2][5005]={0};
  long long ce[5005]={0},cl[5005]={0},ncl[5005]={0};
  
  scanf("%lld%lld%lld",&n,&a,&b);
  r=power(2,n);
  
  if(a<b){llswap(&a,&b);}
  ce[0]=1;
  cl[0]=1;
  for(i=1;i<=a;i++){
    for(j=i-1;j>=0;j--){
      ncl[j+1]+=cl[j];
      ncl[j+1]%=mod;
      if((j+1)>=b){
        ce[i]+=cl[j];
        ce[i]%=mod;
      }
      if(j>=b){
        ncl[0]+=cl[j];
        ncl[0]%=mod;
      }
    }
    ncl[0]+=cl[0];ncl[0]%=mod;
    ce[i]+=ncl[0];ce[i]%=mod;
    for(j=0;j<=i;j++){
      cl[j]=ncl[j];
      ncl[j]=0;
      //printf("[%lld]",cl[j]);
    }//printf("\n");
    //printf("<%lld>\n",ce[i]);
  }

  dp[0][0]=1;
  dp[1][0]=1;
  for(i=0;i<=n;i++){
    //printf("%lld : <%lld %lld>\n",i,dp[0][i],dp[1][i]);
    for(j=1;j<a;j++){
      if((i+j)>n){break;}
      pt=j-2;
      if(i==0){pt++;}
      if(i+j==n){pt++;}
      if(pt<0){dp[0][i+j]+=dp[1][i];}
      else{dp[0][i+j]+=ce[pt]*dp[1][i];}
      dp[0][i+j]%=mod;
    }
    for(j=1;j<b;j++){
      if((i+j)>n){break;}
      dp[1][i+j]+=dp[0][i];
      dp[1][i+j]%=mod;
    }
  }
  r+=mod;r-=dp[0][n];
  r+=mod;r-=dp[1][n];
  printf("%lld\n",r%mod);
  return 0;
}