51nod1799 二分答案(分块打表)

分析：

要走到一个位置的话一共要往左或者往右走O(logn)次，而且每一步都必须走对。因为对于题目中给出的代码，

无论k是什么样的数，二分过程的次数都是固定的。每走一步只和amid的大小关系有关，因此有一些位置只能放≤m

或者>m 的数，其他位置可以随便放。阶乘可以分段打表。


#include<bits/stdc++.h>
using namespace std;
#define LL long long
#define N 105
const int mod = 1e9+7;
const int lim = 1e7;
LL n, m, k;
LL fac
= {1,682498929,491101308,76479948,723816384,67347853,27368307,625544428,199888908,888050723,927880474,281863274,661224977,623534362,970055531,261384175,195888993,66404266,547665832,109838563,933245637,724691727,368925948,268838846,136026497,112390913,135498044,217544623,419363534,500780548,668123525,128487469,30977140,522049725,309058615,386027524,189239124,148528617,940567523,917084264,429277690,996164327,358655417,568392357,780072518,462639908,275105629,909210595,99199382,703397904,733333339,97830135,608823837,256141983,141827977,696628828,637939935,811575797,848924691,131772368,724464507,272814771,326159309,456152084,903466878,92255682,769795511,373745190,606241871,825871994,957939114,435887178,852304035,663307737,375297772,217598709,624148346,671734977,624500515,748510389,203191898,423951674,629786193,672850561,814362881,823845496,116667533,256473217,627655552,245795606,586445753,172114298,193781724,778983779,83868974,315103615,965785236,492741665,377329025,847549272,698611116};
LL GetFact(LL x)
{
LL ret = fac[x/lim];
for(LL i=x/lim*lim+1; i<=x; i++) ret = ret*i%mod;
return ret;
}
void solve()
{
LL left = 1, right = n, mid, cl = 0, cr = 0;
while(left <= right)
{
mid = (left+right)>>1;
if(mid<=k) cl++, left = mid+1;
else cr++, right = mid-1;
}
LL ans = 1;
for(LL i = m; i >= m-cl+1; i--) ans = ans*i%mod;
for(LL i = n-m; i >= n-m-cr+1; i--) ans = ans*i%mod;
ans = ans*GetFact(n-cl-cr) % mod;
cout<<ans<<endl;
}
int main()
{
while(cin>>n>>m>>k)
{
solve();
}
return 0;
}