Problem:
Score : 400 points

Problem Statement

You are given integers N and M.

Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

N \leq M \leq 10^9

Input

Input is given from Standard Input in the following format:

N M

Output

Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.

Sample Input 1

3 14

Sample Output 1

2

Consider the sequence (a_1, a_2, a_3) = (2, 4, 8). Their greatest common divisor is 2, and this is the maximum value.

Sample Input 2

10 123

Sample Output 2

3

Sample Input 3

100000 1000000000

Sample Output 3

10000

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <vector>
#include <map>
#include <set>
#include <cmath>
#include <iostream>
#include <algorithm>
#include <queue>
#include <iomanip>
#include <list>
#include <string>

typedef char                SINT8;
typedef short               SINT16;
typedef int                 SINT32;
typedef long long           SINT64;
typedef double              DOUBLE;

#define MAX(a,b) ((a)>(b)?(a):(b))
#define MIN(a,b) ((a)<(b)?(a):(b))
#define ABS(a) ((a)>(0)?(a):-(a))
#define rep(i,a,b) for(SINT64 (i)=SINT64(a);(i)<SINT64(b);(i)++)
#define rrep(i,a,b) for(SINT64 (i)=SINT64(a);(i)>=SINT64(b);(i)--)

#define put(a) cout << (a) << endl
#define puts(a) cout << (a) << " "

#define putr(a) rep(testIncrement,0,a.size()) {puts(a[testIncrement]);} cout << endl
#define putrr(a) rep(Incr1,0,a.size()) {rep(Incr2,0,a[Incr1].size()) {puts(a[Incr1][Incr2]);} cout<<endl;} cout<<endl;


#define INF 1000000001
#define MOD 1000000007
#define INF64 1000000000000000001

#define F first
#define S second

#define Pii  pair<SINT32,SINT32>
#define Pll  pair<SINT64,SINT64>
#define Piii pair<SINT32,pair<SINT32,SINT32>>
#define Plll pair<SINT64,pair<SINT64,SINT64>>

#define Vll(a,b,c)    vector<vector<SINT64>> (a)((b),vector<SINT64>((c))
#define Vlll(a,b,c,d) vector<vector<vector<SINT64>>> (a)((b),vector<vector<SINT64>>((c),vector<SINT64>((d)))


using namespace std;

int main() {

	SINT64 N;	cin >> N;
	SINT64 M;	cin >> M;

	SINT64 ans = 1;
	vector<SINT64> data;

	rep(i,1,1000005) {
		if ((M%i) == 0) {
			if ((M/i) >= N) {
				ans = i;
			}
			data.emplace_back(M/i);
		}
		
		if (i*i > M) {
			break;
		}
	}
	rep(i,0,data.size()) {
		if ((M/data[i]) >= N) {
			ans = MAX(ans,data[i]);
		}
	}

	put(ans);
	
	return 0;
}


//	vector<vector<SINT64>> data(N,vector<SINT64>(N));										//2次元配列
//	vector<vector<vector<SINT64>>> data(N,vector<vector<SINT64>>(N,vector<SINT64>(N)));		//3次元配列

//	Vll(data,N,N);		//2次元配列
//	Vlll(data,N,N,N);	//3次元配列

//	sort(data.begin(),data.end());
//	sort(data.begin(),data.end(),std::greater<SINT64>());
//	__gcd(A,B);

//  reverse(data.begin(),data.end());

//関数へのvectorポインタ渡し
//void dfs(SINT64 poi, SINT64 d, vector<vector<Pll>>& data) {
//}

/* 複数条件ソート
bool sortcompare(Pll A, Pll B) {
    if(A.F == B.F){
        return A.S > B.S;
    } else {
        return A.F < B.F;
    }
}

sort(data.begin(),data.end(),sortcompare);
*/

// タプル
//vector<tuple<SINT64,SINT64,SINT64>> edges;
//edges.emplace_back(a,b,c);
//cout << get<0>(edges[i]);
//cout << get<1>(edges[i]);
//cout << get<2>(edges[i]);
//sort(begin(edges), end(edges)); //ソート


//	data.emplace_back(BUF);			//後ろに追加

//  data.erase(std::unique(data.begin(), data.end()), data.end());	//ソート後に使用 同じ値を消す

//	data.insert(data.begin() + X, 0);	//X番目の要素に0を挿入


//	隣接リスト
//	vector<vector<SINT64>> data(N);
//	data[ A ].emplace_back( B );


// 両端キュー
//deque<SINT64> data;
//data.emplace_front(buf);	//先頭挿入


// lower_boundは値がなければ最大値(.size())を返す
// posi = lower_bound(data.begin(),data.end(), X) - data.begin();				// X以上を探す
// posi = lower_bound(data.begin(),data.end(),make_pair(X,0)) - data.begin();	//pair


/* 文字列回転
	string N;
	cin >> N;
	N = N[N.length()-1] + N.substr(0,N.length()-1);

	s = to_string(i);	//ストリング変換
*/
/* 文字列合成
	string N,M;
	cin >> N >> M;
	SINT64 ans = 0;
	ans = stoi(N+M);
*/

/*  文字列変更
	string s;	cin >> s;
	rep(i,0,s.length()) {	
		s[i] = (((s[i]-'A' + N) % 26) + 'A');
	}
	put(s);
*/

/*
//ワーシャルフロイド
	vector<vector<SINT64>> dist(N,vector<SINT64>(N,INF64));
	rep(i,0,N) {
		dist[i][i] = 0;
	}
	rep(k,0,N) {
		rep(i,0,N) {
			rep(j,0,N) {
				dist[i][j] = MIN(dist[i][j], dist[i][k]+dist[k][j]);
			}
		}
	}
*/

/*  優先度付きキュー
	priority_queue<SINT64, vector<SINT64>, greater<SINT64>> bufq;	//小さいほうから取り出せる
	priority_queue<SINT64, vector<SINT64>> bufq;					//大きいほうから取り出せる

	bufq.push(X);	//X を挿入
	bufq.top();		//先頭データ読み
	bufq.pop();		//先頭データ削除
*/

/* キュー
	queue<SINT64> bufq;	//宣言
	bufq.push(0);	//挿入
	bufq.front();	//先頭データ読み
	bufq.pop();		//先頭データ削除
*/





/* SET コンテナ
	set<SINT64> data;
	data.insert(X);				//X を挿入
	data.erase(data.begin());	//先頭を削除
	data.erase(--data.end());	//末尾を削除
	*data.begin();				//先頭要素にアクセス
	*data.rbegin();				//末尾要素にアクセス

	//全表示
    set<SINT64>::iterator it; //イテレータを用意
    for(it = data.begin(); it != data.end(); it++) {
        cout << *it << " ";
    }
	cout << endl;

	//N番目を一部表示
	set<SINT64>::iterator it; //  イテレータを用意
	it = data.begin();
	rep (i,0,N) {
		it++;
	}
	cout << *it << endl;
*/

/* map
	map<string,SINT32> mp;
	SINT32 N = 0;
	SINT32 mx = 0;

	cin >> N;
	for (SINT32 i = 0; i < N; i++) {
		string s;
		cin >> s;
		mp[s]++;
	}
	for(auto it=mp.begin();it!=mp.end();it++) {
		mx=max(mx,it->second);
	}

	//abc146E
	map<SINT64,SINT64> mp;
	rep(i,0,N+1) {
		ans += mp[rui[i]];
		mp[rui[i]]++;
		bufq.push(rui[i]);
		if (bufq.size() == M) {
			mp[bufq.front()]--;
			bufq.pop();
		}
	}
*/

/*
	//順列全表示
	//sortしてからでないと全列挙にならない
	sort(data.begin(),data.end());
	do {
		cout << buf << endl;
		rep(i,0,R) {
			cout << data[i] << " ";
		}
		cout << endl;

    } while (next_permutation(data.begin(),data.end()));
*/

/* bit数数え上げ
SINT64 bits64(SINT64 bits)
{
    bits = (bits & 0x55555555) + (bits >> 1 & 0x55555555);
    bits = (bits & 0x33333333) + (bits >> 2 & 0x33333333);
    bits = (bits & 0x0f0f0f0f) + (bits >> 4 & 0x0f0f0f0f);
    bits = (bits & 0x00ff00ff) + (bits >> 8 & 0x00ff00ff);
    return (bits & 0x0000ffff) + (bits >>16 & 0x0000ffff);
}
*/

//bitシフトのLONG対応
// ans += (1L<<50);



//  桁指定表示
//  ans = ans * M_PI;
//	cout << setprecision(15) << ans << endl;

// 桁数0埋め
// cout << std::setfill('0') << std::right << std::setw(2) << 5; //05


//2次元累積和
/*
	vector<vector<SINT64>> data(H,vector<SINT64>(W));
	vector<vector<SINT64>> rui(H+1,vector<SINT64>(W+1));
	
	rep(i,0,H) {
		rep(j,0,W) {
			cin >> data[i][j];
		}
	}
	rep(i,1,H+1) {
		rep(j,1,W+1) {
			rui[i][j] = data[i-1][j-1] + rui[i][j-1];
		}
	}
	rep(i,1,H+1) {
		rep(j,1,W+1) {
			rui[i][j] += rui[i-1][j];
		}
	}
*/


// 逆元　コンビネーション
/*
SINT64 modpow(SINT64 a, SINT64 p) {
	if (p == 0) return 1;
	if (p % 2 == 0) {
		//pが偶数の時
		SINT64 halfP = p / 2;
		SINT64 half = modpow(a, halfP);
		//a^(p/2) をhalfとして、half*halfを計算
		return half * half % MOD;
	} else {
		//pが奇数の時は、偶数にするために1減らす
		return a * modpow(a, p - 1) % MOD;
	}
}

SINT64 calcComb(SINT64 a, SINT64 b) {
	SINT64 Mul = 1;
	SINT64 Div = 1;
	SINT64 ans = 0;

	if (b > a - b) {
		return calcComb(a, a - b);
	}
 
	rep(i,0,b) {
		Mul *= (a - i);
		Div *= (i + 1);
		Mul %= MOD;
		Div %= MOD;
	}
	ans = Mul * modpow(Div, MOD - 2) % MOD;
	return ans;
}
*/


/* UNION FIND
class UnionFind {
public:
	vector<SINT64> parent;

	UnionFind(SINT64 N) {
		parent = vector<SINT64>(N+10, -1);	//少し多めに
	}
	
	SINT64 root(SINT64 A) {
		if (parent[A] < 0) {
			return A;
		} else {
			parent[A] = root(parent[A]);
			return parent[A];
		}
	}

	SINT64 size(SINT64 A) {
		return parent[root(A)] * (-1);
	}

	bool judge(SINT64 A, SINT64 B) {
		A = root(A);
		B = root(B);
		if (A == B) {
			return true;	//同じグループ
		} else {
			return false;	//違うグループ
		}
	}

	void connect(SINT64 A, SINT64 B) {
		A = root(A);
		B = root(B);
		if (A != B) {
			if (size(A) < size(B)) {
				swap(A, B);
			}
			parent[A] += parent[B];
			parent[B] = A;
		}
	}
};
UnionFind uni(N);
 */

/*　セグ木
class SegTree {
private:
	SINT64 size;
	vector<SINT64> node;

	SINT64 jugdement(SINT64 a, SINT64 b) {
		SINT64 ans = 0;
		ans = a+b;
		return ans;
	}

public:

	//コンストラクタ
	SegTree(vector<SINT64> data) {
		SINT64 ori_size;
		ori_size = data.size();
		size = 1;
		while (size < ori_size) {
			size *= 2;
		}
		node.resize(2*size-1, 0);

		rep(i,0,ori_size) {
			node[size-1+i] = data[i];
		}
		rrep(i,size-2,0) {
			node[i] = jugdement(node[2*i+1], node[2*i+2]);
		}
	}

	//データ更新
	void update(SINT64 x, SINT64 val) {
		x += (size - 1);
    	node[x] = val+node[x];
    	while(x > 0) {
        	x = (x - 1) / 2;
        	node[x] = jugdement(node[2*x+1], node[2*x+2]);
		}
	}

	//データ取得 [a,b)
	SINT64 getdata(SINT64 a, SINT64 b, SINT64 k = 0, SINT64 l = 0, SINT64 r = -1) {
		if (r < 0) {
			r = size;
		}

		//要求範囲外
		if ((r <= a) || (b <= l)) {
			return 0;
		}
		//完全要求区間内
		if ((a <= l) && (r <= b)) {
			return node[k];
		}

    	SINT64 vl = getdata(a, b, 2*k+1, l, (l+r)/2);
    	SINT64 vr = getdata(a, b, 2*k+2, (l+r)/2, r);
    	return jugdement(vl, vr);
	}

	//表示
	void disp() {
		rep(i,0,size) {
			puts(node[size-1+i]);
		} cout << endl;
	}

	void alldisp() {
		SINT64 cnt = 0;
		SINT64 end = 2;
		
		while (1) {
			puts(node[cnt]);
			if (cnt == end-2) {
				end *= 2;
				cout << endl;
			}
			cnt++;
			if (cnt == size*2-1) {
				break;
			}
		}	
	}
};

SegTree seg(N);
 */

/* 最大フロー最小カット
class Dinic {
	struct EDGE {
		SINT64 to;
		SINT64 cap;
		SINT64 rev;
	};
	vector<vector<EDGE>> G;
	vector<SINT64> level;
	vector<SINT64> root;
	SINT64 N;
 
public:
	Dinic(SINT64 n) {
		N = n;
		G.resize(N);
		level.resize(N);
	}
	
	void add(SINT64 a, SINT64 b, SINT64 cap) {
		G[a].emplace_back((EDGE){b,cap,(SINT64)G[b].size()});
		G[b].emplace_back((EDGE){a,0,(SINT64)G[a].size()-1});
	}
 
	void bfs(SINT64 s) {
		level[s] = 0;
		queue<SINT64> q;
		q.push(s);
		while(q.size() != 0) {
			SINT64 buf = q.front();
			q.pop();
			rep(i,0,G[buf].size()) {
				EDGE now = G[buf][i];
				if ((now.cap > 0) && (level[now.to] == -1)) {
					level[now.to] = level[buf]+1;
					q.push(now.to);
				}
			}
		}
	}
 
	SINT64 dfs(SINT64 now, SINT64 g, SINT64 flow) {
		if (now == g) return flow;
		rep(i,root[now],G[now].size()) {
			EDGE buf = G[now][i];
			root[now] = i;							//dsf進捗更新
			if ((buf.cap > 0) && (level[buf.to] > level[now])) {
				SINT64 mi = MIN(buf.cap,flow);
				SINT64 nowf = dfs(buf.to,g,mi);
				if (nowf > 0) {
					G[now][i].cap -= nowf;			//順経路に容量削減
					G[buf.to][buf.rev].cap += nowf;	//逆経路に容量追加
					return nowf;					//今回探索のFLOW追加数
				}
			}
		}
		return 0;
	}
 
	SINT64 act(SINT64 s, SINT64 g) {
		SINT64 cnt = 0;								//最大FLOWカウント
		if (s == g) return cnt;						//スタート＝ゴールは例外
		while(1) {
			level.assign(N,-1);						//sからの最短距離初期化
			root.assign(N,0);						//dsf進捗初期化
			bfs(s);
			if (level[g] == -1) break;				//gへ到達不可
			while(1) {
				SINT64 flow;
				flow = dfs(s,g,INF64);
				if (flow == 0) break;
				cnt += flow;
			}
		}
		return cnt;
	}
};
*/

/* ダイクストラ
class Dijkstra {	
	vector<vector<Pll>> G;
	vector<SINT64> dist;
 
public:
	Dijkstra(SINT64 n) {
		G.resize(n);
		dist.resize(n, INF64);
	}
	
	void add(SINT64 a, SINT64 b, SINT64 cost) {
		G[a].emplace_back(Pll(b,cost));
	}

	void form(SINT64 s) {
		priority_queue<Pll, vector<Pll>, greater<Pll>> q;
		q.push(Pll(0,s));						//cost,位置
		while(q.size() != 0) {
			Pll now = q.top();
			q.pop();
			if (dist[now.S] == INF64) {
				dist[now.S] = now.F;
				rep(i,0,G[now.S].size()) {
					Pll buf = G[now.S][i];
					if (dist[buf.F] == INF64) {
						q.push(Pll(buf.S+now.F,buf.F));
					}
				}
			}
		}
	}
	
	//form()で構築したsからの距離を返す
	SINT64 get_dist(SINT64 a) {
		if (dist[a] == INF64) {
			return -1;			//到達不可
		} else {
			return dist[a];
		}
	}
};
*/

/* LCA
class Lca {
	vector<vector<SINT64>> G;
	vector<vector<SINT64>> D;	//ダブリング
	vector<SINT64> depth;
	SINT64 N;
	SINT64 LOG_N;
 
public:
	Lca(SINT64 n) {
		N = n;
		LOG_N = floor(log2(N));
		G.resize(N);
		D.resize(N);
		depth.resize(N,-1);
	}
	
	void add(SINT64 a, SINT64 b) {
		G[a].emplace_back(b);
		G[b].emplace_back(a);
	}
 
	void bfs(SINT64 s) {
		depth[s] = 0;
		D[s].emplace_back(-1);
		queue<SINT64> q;
		q.push(s);
		while(q.size() != 0) {
			SINT64 now = q.front();
			q.pop();
			rep(i,0,G[now].size()) {
				SINT64 next = G[now][i];
				if (depth[next] == -1) {
					depth[next] = depth[now]+1;
					D[next].emplace_back(now);
					q.push(next);
				}
			}
		}
	}
 
	//頂点のsからのダブリング構築
	void form(SINT64 s) {
		bfs(s);
		rep(i,1,LOG_N+1) {
			rep(j,0,N) {
				SINT64 buf = D[j][i-1];
				if (buf == -1) {
					D[j].emplace_back(-1);
				} else {
					D[j].emplace_back(D[buf][i-1]);
				}
			}
		}
	}
 
	//aのx上の頂点を求める
	SINT64 get(SINT64 a, SINT64 x) {	
		rrep(i,LOG_N,0) {
			if (((x >> i) & 1) == 1) {
				a = D[a][i];
				if (a == -1) return -1;
			}
		}
		return a;
	}
 
	//aとbの共通祖先を求める
	SINT64 get_lca(SINT64 a, SINT64 b) {
		if (depth[a] < depth[b]) swap(a,b);
		SINT64 diff = depth[a] - depth[b];
		a = get(a,diff);					//aのx上の頂点を求める
		if (a == b) return a;
		rrep(i,LOG_N,0) {
			if (D[a][i] != D[b][i]) {
				a = D[a][i];
				b = D[b][i];
			}
		}	
		return D[a][0];
	}

	//aとbの共通祖先までの距離の合計を求める
	SINT64 get_dist(SINT64 a, SINT64 b) {
		SINT64 buf = get_lca(a,b);
		return depth[a] + depth[b] - depth[buf]*2;
	}
};
*/

/* ベルマンフォード
class Bellman {
	struct EDGE {
		SINT64 from;
		SINT64 to;
		SINT64 cost;
	};
	vector<EDGE> edges;
	vector<SINT64> dist;
	SINT64 N;
 
public:
	Bellman(SINT64 n) {
		N = n;
		dist.resize(n, INF64);
	}
	
	void add(SINT64 from, SINT64 to, SINT64 cost) {
		edges.emplace_back((EDGE){from,to,cost});
	}
 
	//sで構築したt迄の距離取得
	SINT64 get_dist(SINT64 t) {
		//到達不可はINF64
		return dist[t];
	}
 
	//構築
	//負の閉路無し : 0
	//負の閉路有り : 1
	//負の閉路有るが目的地gの更新は停止 : 2
	SINT64 form(SINT64 s, SINT64 g) {
		dist[s] = 0;
		SINT64 cnt = 0;
		SINT64 check = 0;
		while(1) {
			SINT64 renew = 0;
			rep(i,0,edges.size()) {
				EDGE e = edges[i];
				if (dist[e.from] != INF64) {
					if (dist[e.to] > dist[e.from] + e.cost) {
						renew = 1;
						dist[e.to] = dist[e.from] + e.cost;
					}
				}
			}
			if (renew == 0) return 0;

			//N回更新後のgの距離と 2N回更新後のgの距離を比較
			if (cnt == N) check = dist[g];
			if (cnt > 2*N) {
				if (check == dist[g]) return 2;
				return 1;
			}
			cnt++;
		}
	}
};
*/

/*コンビネーション
class Comb {
	vector<SINT64> base;
	SINT64 N;
 
public:
	Comb (SINT64 n) {
		N = n+5;
		base.resize(N);
		base[0] = 1;
		rep(i,1,N) {
			base[i] = base[i-1]*i;
			base[i] %= MOD;
		}
	}
	
	SINT64 get_comb(SINT64 a, SINT64 b) {
		SINT64 ans = 0;
		SINT64 aa = base[a] * modpow(base[a-b], MOD - 2) % MOD;
		ans = aa * modpow(base[b], MOD - 2) % MOD;
		return ans;
	}

	SINT64 modpow(SINT64 a, SINT64 p) {
		if (p == 0) return 1;
		if (p % 2 == 0) {
			SINT64 halfP = p / 2;
			SINT64 half = modpow(a, halfP);
			return half * half % MOD;
		} else {
			return a * modpow(a, p - 1) % MOD;
		}
	}
};
*/


/* SUFFIX ARRAY
class SuffixArray {
private:
	vector<string> array;			// サフィックスアレイ
	vector<SINT64> lcp;				// LCP
	vector<SINT64> sais;			// SA IS
	string str;
	
public:
	// コンストラクタ
	SuffixArray (string s) {
		str = s;
        vector<SINT64> Vstr;
        rep(i,0,str.length()) {
            Vstr.emplace_back(str[i]);
        }
		sais_act(Vstr, sais, 255);		// SAIS実行
//		lcp_act();						// 隣り合うSUFFIXの先頭から同じ長さを算出

		// suffix array 文字列作成 
//		array.resize(str.length());
//		rep(i,0,array.size()) {
//			array[i] = str.substr(sais[i]);
//		}
//		rep(i,0,array.size()) {put(array[i]);}               // 表示用
	}

	// LCP作成
	void lcp_act(void) {
		lcp.resize(str.length());
		vector<SINT64> buffer(str.length());
		rep(i,0,str.length()) {
			buffer[sais[i]] = i;
		}
 
		SINT64 cnt = 0;
		rep(i,0,str.length()) {
			if (buffer[i] >= str.length()-1) {
				cnt = 0;
				
			} else {
				SINT64 a = buffer[i];
				SINT64 b = buffer[i]+1;
				
				while(1) {
					if (cnt >= str.length() - sais[a]) break;
					if (cnt >= str.length() - sais[a]) break;
					
					if (str[sais[a]+cnt] == str[sais[b]+cnt]) {
						cnt++;
					} else {
						break;
					}
				}
			}
			lcp[buffer[i]] = cnt;
			if (cnt != 0) cnt--;
		}
	}

	// 引数の文字列が何個含まれるか算出
	SINT64 get_cnt(string t) {
		SINT64 low,high;
		SINT64 L,R;
		L = -1;
		R = str.length();
		while(R-L > 1) {
			SINT64 M = (R+L)/2;
			string buf = str.substr(sais[M]);
			if (buf.length() > t.length()) {
				buf = buf.substr(0,t.length());
			}
			if (buf > t) {R = M;} else {L = M;}
		}
		high = R;

		L = -1;
		R = str.length();
		while(R-L > 1) {
			SINT64 M = (R+L)/2;
			string buf = str.substr(sais[M]);
			if (buf >= t) {R = M;} else {L = M;}
		}
		low = R;
		return high - low;
	}
	
	// SAIS実行
	void sais_act(vector<SINT64>& Vstr, vector<SINT64>& r_sais, SINT64 type) {
		Vstr.push_back(0);							// 番兵追加
		vector<SINT64> lms_seed;					// LMS ソート前
		vector<SINT64> lms_sort;					// LMS ソート後
		vector<SINT64> lms_long(Vstr.size(),0);		// LMS 長さ
		vector<SINT64> lms_type(Vstr.size(),1);		// 0:L 1:S 2:LMS
		vector<SINT64> lms_posi(Vstr.size(),-1);		// LMS内での位置
		
		SINT64 len = 0;
		// L S LMS判定 初期値は全てS
		rrep(i,Vstr.size()-2,0) {
			len++;
			if (Vstr[i] > Vstr[i+1]) {
				lms_type[i] = 0;					// L
				if (lms_type[i+1] == 1) {
					lms_type[i+1] = 2;				// LMS
					lms_long[i+1] = len;			// LMSの長さ格納
					len = 1;
				}
			}
			if (Vstr[i] == Vstr[i+1]) lms_type[i] = lms_type[i+1];	// 右と同じ
		}

		SINT64 cnt = 0;
		rep(i,0,Vstr.size()) {
			if (lms_type[i] == 2) lms_seed.emplace_back(i);
			if (lms_type[i] == 2) lms_posi[i] = cnt++;
		}

		// Induced Sort初回
		vector<SINT64> bucket;										// Induced Sort初回結果格納用
		induced_sort(Vstr, lms_seed, bucket, lms_type, type);

		// lms_sortにLMSのソートを格納
		rrep(i,Vstr.size()-1,0) {
			if ((bucket[i] != -1) && (lms_type[bucket[i]] == 2)) {
				lms_sort.emplace_back(bucket[i]);
			}
		}

		SINT64 ok = 0;						        // 再帰必要性判定
		SINT64 rank = 1;					        // 再帰用文字
		vector<SINT64> next(lms_sort.size(), 1);	// 再帰用文字列
					
		rrep(i,lms_sort.size()-2,0) {
            SINT64 A = lms_long[lms_sort[i]];
            SINT64 B = lms_long[lms_sort[i+1]];
			if (A == B) {
                SINT64 ck = 0;
                rep(j,0,A) {
                    if (Vstr[lms_sort[i]+j] != Vstr[lms_sort[i+1]+j]) {
                        ck = 1;
                        break;
                    }
                }
                if (ck == 0) {
                    ok = 1;		// 再帰必要
                } else {
                    rank++;
                }				
			} else {
				rank++;
			}
			next[lms_posi[lms_sort[i]]] = rank;
		}
	
		if (ok == 1) {
			vector<SINT64> recursive;
			sais_act(next, recursive, rank+1);
			rep(i,0,recursive.size()) {
				lms_sort[recursive.size()-i-1] = lms_seed[recursive[i]];
			}
		}
		
		// SORT済みLMSでInduced Sorting
		r_sais.resize(Vstr.size(),-1);
		induced_sort(Vstr, lms_sort, r_sais, lms_type, type);
		r_sais.erase(r_sais.begin());	// 番兵削除   
	}
	
	// induced_sort
	void induced_sort(vector<SINT64>& Vstr, vector<SINT64>& seed, vector<SINT64>& bucket_sort, vector<SINT64>& lms_type, SINT64 type) {
		vector<SINT64> bucket_cnt(type,0);			// バケット 文字種ごとの数
		vector<SINT64> bucket_st(type,0);			// バケット 文字種の開始位置
		vector<SINT64> bucket_end(type,0);			// バケット 文字種の終了位置
		vector<SINT64> bucket_pre(Vstr.size(),-1);	// バケット 初回格納用
		vector<SINT64> cnt1(type,0);
		vector<SINT64> cnt2(type,0);
		vector<SINT64> cnt3(type,0);
		bucket_sort.resize(Vstr.size(),-1);

		// バケットソート位置作成
		rep(i,0,Vstr.size()) bucket_cnt[Vstr[i]]++;						// 個数作成
		rep(i,1,type) bucket_st[i] = bucket_st[i-1] + bucket_cnt[i-1];	// 開始位置
		rep(i,0,type) bucket_end[i] = bucket_st[i] + bucket_cnt[i]-1;	// 終了位置

		// LMSをbucket_preに格納
		rep(i,0,seed.size()) {
			SINT64 no = seed[i];
			bucket_pre[bucket_end[Vstr[no]] - cnt1[Vstr[no]]] = no;
			cnt1[Vstr[no]]++;
		}
		
		// Lをbucket_sortに格納
		rep(i,0,Vstr.size()) {
			if ((bucket_pre[i] != -1) && (bucket_pre[i] != 0)) {
				if (lms_type[bucket_pre[i]-1] == 0) {		// -1がLの場合
					SINT64 buf = Vstr[bucket_pre[i]-1];
					bucket_pre [bucket_st[buf] + cnt2[buf]] = bucket_pre[i]-1;
					bucket_sort[bucket_st[buf] + cnt2[buf]] = bucket_pre[i]-1;
					cnt2[buf]++;
				}
			}
		}
		
		// Sをbucket_sortに格納
		bucket_sort[0] = Vstr.size()-1;						// 番兵追加
		rrep(i,Vstr.size()-1,0) {
			if ((bucket_sort[i] != -1) && (bucket_sort[i] != 0)) {
				if (lms_type[bucket_sort[i]-1] != 0) {		// -1がS(LMS)の場合
					SINT64 buf = Vstr[bucket_sort[i]-1];
					bucket_sort[bucket_end[buf] - cnt3[buf]] = bucket_sort[i]-1;
					cnt3[buf]++;
				}
			}
		}
	}
};
*/


/* 転倒数の数え上げ
SINT64 merge_cnt(vector<SINT64> &a) {
    SINT64 n = a.size();
    if (n <= 1) { return 0; }

    SINT64 cnt = 0;
    vector<SINT64> b(a.begin(), a.begin()+n/2);
    vector<SINT64> c(a.begin()+n/2, a.end());

    cnt += merge_cnt(b);
    cnt += merge_cnt(c);

    SINT64 ai = 0, bi = 0, ci = 0;
    // merge の処理
    while (ai < n) {
        if ( bi < b.size() && (ci == c.size() || b[bi] <= c[ci]) ) {
            a[ai++] = b[bi++];
        } else {
            cnt += n / 2 - bi;
            a[ai++] = c[ci++];
        }
    }
    return cnt;
}
*/