#include <ctime>
#include <cstdlib>
#include <stdio.h>
#include <iostream>
#include <string>
#include <vector>
#include <map>
#include <cmath>
#include <fstream>
using namespace std;
#define NODEMAX 20
class Test {
public:	
	static std::vector<int>nodeMin;
	static std::vector<int>nodeMax;
	static std::vector<int>leafMin;
	static std::vector<int>leafMax;
	static std::map<std::vector<int>,int> tNum;

	static int treeNum(int n,int m,int level){
		std::vector<int> nml;
		nml.push_back(n);
		nml.push_back(m);
		nml.push_back(level);
		std::map<std::vector<int>,int> ::iterator it=tNum.find(nml);
		if(it!=tNum.end())
			return it->second;
		//
		if(level<=1)return 0;
		//if(level<=1||level>=n)return 0;
		int res=0;
		int sumNode=n-1;//左右子树的结点总数
		int minLevel=level-2;//左右子树的最小深度

		for(int leftLevel=minLevel;leftLevel<level;++leftLevel){	
			if(leftLevel<0)continue;
			for(int rightLevel=minLevel;rightLevel<level;++rightLevel){
				if(rightLevel<0)continue;
				if(leftLevel==minLevel&&rightLevel==minLevel)//左右子树深度不能同时为level-2
					continue;
				 for(int leftNode=nodeMin[leftLevel];leftNode<=sumNode&&leftNode<=nodeMax[leftLevel];++leftNode){
					 int rightNode=sumNode-leftNode;
					 if(rightNode>nodeMax[rightLevel])
						 continue;
					 if(rightNode<nodeMin[rightLevel])
						 break;
					 for(int leftLeaf=leafMin[leftLevel];leftLeaf<=leftNode&&leftLeaf<=m&&leftLeaf<=leafMax[leftLevel];++leftLeaf){
						 int rightLeaf=m-leftLeaf;
						 if(rightLeaf>leafMax[rightLevel]||rightLeaf>rightNode)
							 continue;
						 if(rightLeaf<leafMin[rightLevel])
							 break;
						 int leftTree=treeNum(leftNode,leftLeaf,leftLevel);
						 int rightTree=0;
						 if(leftTree)
							 rightTree=treeNum(rightNode,rightLeaf,rightLevel);
						 res+=leftTree*rightTree;
					 }//for
				}//for
			}//for
		}//for

		tNum.insert(make_pair(nml,res));
        return res;
    }

	static int howmany (int   n,int   m){
		static bool firstTime=true;
		if(firstTime){
			firstTime=false;
			nodeMin.push_back(0);
			nodeMin.push_back(1);
			nodeMax.push_back(0);
			nodeMax.push_back(1);
			leafMin.push_back(0);
			leafMin.push_back(1);
			leafMax.push_back(0);
			leafMax.push_back(1);
			int index=nodeMin.size()-1;
			while(nodeMin[index]<NODEMAX){
				nodeMin.push_back(nodeMin[index]+nodeMin[index-1]+1);
				nodeMax.push_back(nodeMax[index]+nodeMax[index]+1);

				leafMin.push_back(leafMin[index]+leafMin[index-1]);
				leafMax.push_back(leafMax[index]+leafMax[index]);

				index=nodeMin.size()-1;
			}//while
			//for(index=0;index<nodeMin.size();++index)
			//	std::cout<<"level="<<index<<":"<<nodeMin[index]<<" "<<nodeMax[index]<<" "<<leafMin[index]<<" "<<leafMax[index]<<std::endl;
			std::vector<int> nml;//ie： n、m、level
			nml.push_back(0);
			nml.push_back(0);
			nml.push_back(0);
			tNum.insert(make_pair(nml,1));
			nml[0]=1;
			nml[1]=1;
			nml[2]=1;
			tNum.insert(make_pair(nml,1));
			/*将第二层中的能构成平衡二叉树的情况提前计算出来，可以减少一次递归次数
			  需要将treeNum中的if(level<=1)修改成if(level<=1||level>=n)return 0;
			nml[0]=2;
			nml[1]=1;
			nml[2]=2;
			tNum.insert(make_pair(nml,2));
			nml[0]=3;
			nml[1]=2;
			nml[2]=2;
			tNum.insert(make_pair(nml,1));
			*/
		}//if(firstTime)

		int res=0;
		for(int level=1;level<leafMin.size();++level)
			if(m>=leafMin[level]&&m<=leafMax[level]&&n>=nodeMin[level]&&n<=nodeMax[level])
				res+=treeNum(n,m,level);		
        return res;
    }
};
std::vector<int>Test::nodeMin;
std::vector<int>Test::nodeMax;
std::vector<int>Test::leafMin;
std::vector<int>Test::leafMax;
std::map<std::vector<int>,int>Test::tNum;

//start 提示：自动阅卷起始唯一标识，请勿删除或增加。
int main(){  
    clock_t t1=clock();

	//C++提交不成功，生成的结果却能提交C成功，感觉英雄会本道题的C++提交有问题
    int n=20,m=20; 
	std::cout<<"int val[21][21]={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0"<<std::endl;;
	for(int n=1;n<=20;++n){
		int m=1;
		std::cout<<",0";
		for(;m<=n;++m){
			//val.insert(make_pair(n,m),Test::howmany(n,m));
			//std::cout<<"n="<<n<<",m="<<m<<" : "<<Test::howmany(n,m)<<endl;
			std::cout<<","<<Test::howmany(n,m);
		}
		for(;m<=20;++m)
			std::cout<<",0";
		std::cout<<std::endl;
	}
		std::cout<<"};"<<std::endl;

    clock_t t2=clock();
    std::cout<<(t2-t1)/(double)CLOCKS_PER_SEC<<" s"<<std::endl;
} 
//end //提示：自动阅卷结束唯一标识，请勿删除或增加。