import sys readline=sys.stdin.readline import math from collections import defaultdict def Extended_Euclid(n,m): stack=[] while m: stack.append((n,m)) n,m=m,n%m if n>=0: x,y=1,0 else: x,y=-1,0 for i in range(len(stack)-1,-1,-1): n,m=stack[i] x,y=y,x-(n//m)*y return x,y class MOD: def __init__(self,p,e=None): self.p=p self.e=e if self.e==None: self.mod=self.p else: self.mod=self.p**self.e def Pow(self,a,n): a%=self.mod if n>=0: return pow(a,n,self.mod) else: #assert math.gcd(a,self.mod)==1 x=Extended_Euclid(a,self.mod)[0] return pow(x,-n,self.mod) def Build_Fact(self,N): assert N>=0 self.factorial=[1] if self.e==None: for i in range(1,N+1): self.factorial.append(self.factorial[-1]*i%self.mod) else: self.cnt=[0]*(N+1) for i in range(1,N+1): self.cnt[i]=self.cnt[i-1] ii=i while ii%self.p==0: ii//=self.p self.cnt[i]+=1 self.factorial.append(self.factorial[-1]*ii%self.mod) self.factorial_inve=[None]*(N+1) self.factorial_inve[-1]=self.Pow(self.factorial[-1],-1) for i in range(N-1,-1,-1): ii=i+1 while ii%self.p==0: ii//=self.p self.factorial_inve[i]=(self.factorial_inve[i+1]*ii)%self.mod def Build_Inverse(self,N): self.inverse=[None]*(N+1) assert self.p>N self.inverse[1]=1 for n in range(2,N+1): if n%self.p==0: continue a,b=divmod(self.mod,n) self.inverse[n]=(-a*self.inverse[b])%self.mod def Inverse(self,n): return self.inverse[n] def Fact(self,N): if N<0: return 0 retu=self.factorial[N] if self.e!=None and self.cnt[N]: retu*=pow(self.p,self.cnt[N],self.mod)%self.mod retu%=self.mod return retu def Fact_Inve(self,N): if self.e!=None and self.cnt[N]: return None return self.factorial_inve[N] def Comb(self,N,K,divisible_count=False): if K<0 or K>N: return 0 retu=self.factorial[N]*self.factorial_inve[K]%self.mod*self.factorial_inve[N-K]%self.mod if self.e!=None: cnt=self.cnt[N]-self.cnt[N-K]-self.cnt[K] if divisible_count: return retu,cnt else: retu*=pow(self.p,cnt,self.mod) retu%=self.mod return retu class Prime: def __init__(self,N): assert N<=10**8 self.smallest_prime_factor=[None]*(N+1) for i in range(2,N+1,2): self.smallest_prime_factor[i]=2 n=int(N**.5)+1 for p in range(3,n,2): if self.smallest_prime_factor[p]==None: self.smallest_prime_factor[p]=p for i in range(p**2,N+1,2*p): if self.smallest_prime_factor[i]==None: self.smallest_prime_factor[i]=p for p in range(n,N+1): if self.smallest_prime_factor[p]==None: self.smallest_prime_factor[p]=p self.primes=[p for p in range(N+1) if p==self.smallest_prime_factor[p]] def Factorize(self,N): assert N>=1 factors=defaultdict(int) if N<=len(self.smallest_prime_factor)-1: while N!=1: factors[self.smallest_prime_factor[N]]+=1 N//=self.smallest_prime_factor[N] else: for p in self.primes: while N%p==0: N//=p factors[p]+=1 if N
0 divisors=[1] for p,e in self.Factorize(N).items(): pow_p=[1] for _ in range(e): pow_p.append(pow_p[-1]*p) divisors=[i*j for i in divisors for j in pow_p] return divisors def Is_Prime(self,N): return N==self.smallest_prime_factor[N] def Totient(self,N): for p in self.Factorize(N).keys(): N*=p-1 N//=p return N def Mebius(self,N): fact=self.Factorize(N) for e in fact.values(): if e>=2: return 0 else: if len(fact)%2==0: return 1 else: return -1 def CRT(remainder_lst,mod_lst): assert len(remainder_lst)==len(mod_lst) if not remainder_lst: return 0,1 remainder,mod=remainder_lst[0],mod_lst[0] for r,m in zip(remainder_lst[1:],mod_lst[1:]): if (r,m)==(-1,0): remainder,mod=-1,0 break r%=m g=math.gcd(mod,m) lcm=LCM(mod,m) if remainder%g!=r%g: remainder,mod=-1,0 break remainder,mod=(r+m*((remainder-r)//g)*Extended_Euclid(m//g,mod//g)[0])%lcm,lcm return remainder,mod def LCM(n,m): if n or m: return abs(n)*abs(m)//math.gcd(n,m) return 0 class Lucas_Prime: def __init__(self,P,e=1): self.P=P self.e=e self.mod=self.P**self.e self.factorial=[1] for i in range(1,self.mod): self.factorial.append(self.factorial[-1]) if i%P: self.factorial[i]*=i self.factorial[i]%=self.mod def Comb(self,N,K,divisible_count=False): if K<0 or K>N: return 0 K0,K1=K,N-K N_lst=[] N_=N while N_: N_lst.append(N_%self.mod) N_//=self.P K0_lst=[] K0_=K0 for _ in range(len(N_lst)): K0_lst.append(K0_%self.mod) K0_//=self.P K1_lst=[] K1_=K1 for _ in range(len(N_lst)): K1_lst.append(K1_%self.mod) K1_//=self.P retu,retu_rev=1,1 for n in N_lst: retu*=self.factorial[n] retu%=self.mod for k0 in K0_lst: retu_rev*=self.factorial[k0] retu_rev%=self.mod for k1 in K1_lst: retu_rev*=self.factorial[k1] retu_rev%=self.mod retu*=MOD(self.mod).Pow(retu_rev,-1) if self.P!=2 or self.e<=2: cnt=0 N_=N//self.mod K0_=K0//self.mod K1_=K1//self.mod while N_: cnt+=N_ N_//=self.P while K0_: cnt+=K0_ K0_//=self.P while K1_: cnt+=K1_ K1_//=self.P if cnt%2==1: retu*=-1 retu%=self.mod div_cnt=0 N_,K0_,K1_=N,K0,K1 while N_: div_cnt+=N_ N_//=self.P while K0_: div_cnt-=K0_ K0_//=self.P while K1_: div_cnt-=K1_ K1_//=self.P if divisible_count: return retu,div_cnt else: retu*=pow(self.P,div_cnt,self.mod) retu%=self.mod return retu class Lucas: def __init__(self,mod): self.mod=mod P=Prime(int(self.mod**.5)) self.factorize=[(p,e) for p,e in P.Factorize(mod).items()] self.LP=[(p,e,Lucas_Prime(p,e)) for p,e in self.factorize] def Comb(self,N,K): lst_r=[] lst_m=[] for p,e,lp in self.LP: lst_r.append(lp.Comb(N,K)) lst_m.append(p**e) r,_=CRT(lst_r,lst_m) return r L,R,M=map(int,readline().split()) Lu=Lucas(M) ans=0 for m in range(L,R+1): ans+=Lu.Comb(2*m,m)-2 ans%=M print(ans)