[BZOJ3160]万径人踪灭

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <stack>
#include <vector>
#include <queue>
#include <cstring>
#include <string>
#include <map>
#include <set>
using namespace std;

const int BufferSize = 1 << 16;
char buffer[BufferSize], *Head, *Tail;
inline char Getchar() {
	if(Head == Tail) {
		int l = fread(buffer, 1, BufferSize, stdin);
		Tail = (Head = buffer) + l;
	}
	return *Head++;
}
int read() {
	int x = 0, f = 1; char c = Getchar();
	while(!isdigit(c)){ if(c == ‘-‘) f = -1; c = Getchar(); }
	while(isdigit(c)){ x = x * 10 + c - ‘0‘; c = Getchar(); }
	return x * f;
}

#define maxn 260010
#define MOD 1000000007
#define ULL unsigned long long
const double pi = acos(-1.0);
int n;
ULL hashl[maxn], hashr[maxn], hashl2[maxn], hashr2[maxn], id2[maxn], id3[maxn];
char S[maxn];
struct Complex {
	double a, b;
	Complex() { a = b = 0.0; }
	Complex operator + (const Complex& t) const {
		Complex ans;
		ans.a = a + t.a;
		ans.b = b + t.b;
		return ans;
	}
	Complex operator - (const Complex& t) const {
		Complex ans;
		ans.a = a - t.a;
		ans.b = b - t.b;
		return ans;
	}
	Complex operator * (const Complex& t) const {
		Complex ans;
		ans.a = a * t.a - b * t.b;
		ans.b = a * t.b + b * t.a;
		return ans;
	}
	Complex operator *= (const Complex& t) {
		*this = *this * t;
		return *this;
	}
} a[maxn<<1], b[maxn<<1];

int tar[maxn];
void FFT(Complex* a, int n, int tp) {
	for(int i = 0; i < n; i++) if(i < tar[i]) swap(a[i], a[tar[i]]);
	for(int i = 1; i < n; i <<= 1) {
		Complex w, wn; wn.a = cos(pi / i); wn.b = sin(pi / i) * tp;
		for(int j = 0; j < n; j += (i << 1)) {
			w.a = 1.0; w.b = 0.0;
			for(int k = 0; k < i; k++) {
				Complex t1 = a[j+k], t2 = a[j+k+i] * w;
				a[j+k] = t1 + t2;
				a[j+k+i] = t1 - t2;
				w *= wn;
			}
		}
	}
	if(tp < 0) for(int i = 0; i <= n; i++) a[i].a = a[i].a / (double)n + .5;
	return ;
}

ULL lstr(int l, int r) { l++, r++; return hashl[r] - hashl[l-1] * id2[r-l+1]; }
ULL rstr(int l, int r) { l++, r++; return hashr[l] - hashr[r+1] * id2[r-l+1]; }
ULL lstr2(int l, int r) { l++, r++; return hashl2[r] - hashl2[l-1] * id3[r-l+1]; }
ULL rstr2(int l, int r) { l++, r++; return hashr2[l] - hashr2[r+1] * id3[r-l+1]; }

int two[maxn], ans, Len;
bool check(int i, int mid) {
	int ll = (i >> 1) - mid + 1, lr = (i >> 1), rl = (i & 1) ? (i >> 1) + 1 : lr, rr = rl + mid - 1;
	bool res = ll >= 0 && rr < Len && (rstr(ll, lr) == lstr(rl, rr)) && (rstr2(ll, lr) == lstr2(rl, rr));
//	if((i >> 1) == 127) printf("%d(%c) %d(%c) %d(%c) %d(%c) %llu %llu\t", ll, S[ll], lr, S[lr], rl, S[rl], rr, S[rr], rstr(ll, lr), lstr(rl, rr));
	return ll >= 0 && rr < Len && rstr(ll, lr) == lstr(rl, rr) && rstr2(ll, lr) == lstr2(rl, rr);
}
int main() {
	scanf("%s", S);
	int m = strlen(S) - 1; Len = strlen(S);
	
	int L = 0;
	for(n = 1; n <= (m << 1); n <<= 1) L++;
	for(int i = 0; i < n; i++) tar[i] = (tar[i>>1] >> 1) | ((i & 1) << L - 1);
	for(int i = 0; i <= m; i++) a[i].a = (double)(S[i] == ‘a‘);
	FFT(a, n, 1);
	for(int i = 0; i <= n; i++) a[i] *= a[i];
	for(int i = 0; i <= m; i++) b[i].a = (double)(S[i] == ‘b‘);
	FFT(b, n, 1);
	for(int i = 0; i <= n; i++) b[i] *= b[i], a[i] = a[i] + b[i];
	FFT(a, n, -1);
	for(int i = 0; i <= (m << 1); i++) a[i].a = (double)((int)a[i].a + 1 >> 1), b[i].a = (double)((int)b[i].a + 1 >> 1);
//	for(int i = 0; i <= (m << 1); i++) printf("%d ", (int)a[i].a); putchar(‘\n‘);
	
	two[0] = 1;
	for(int i = 1; i <= m; i++) {
		two[i] = two[i-1] << 1;
		if(two[i] > MOD) two[i] -= MOD;
	}
	hashl[0] = 0;
	for(int i = 1; i <= m + 1; i++) hashl[i] = hashl[i-1] * 2 + S[i-1] - ‘a‘;
	hashr[m+2] = 0;
	for(int i = m + 1; i; i--) hashr[i] = hashr[i+1] * 2 + S[i-1] - ‘a‘;
	id2[0] = 1;
	for(int i = 1; i <= m + 1; i++) id2[i] = id2[i-1] * 2;
	hashl2[0] = 0;
	for(int i = 1; i <= m + 1; i++) hashl2[i] = hashl2[i-1] * 3 + S[i-1] - ‘a‘;
	hashr2[m+2] = 0;
	for(int i = m + 1; i; i--) hashr2[i] = hashr2[i+1] * 3 + S[i-1] - ‘a‘;
	id3[0] = 1;
	for(int i = 1; i <= m + 1; i++) id3[i] = id3[i-1] * 3;
	m++, m <<= 1; int tmp = 0;
	for(int i = 0; i <= m - 2; i++) {
		ans += two[(int)a[i].a];
		int l = 0, r = min((i >> 1) + 1, (i & 1) ? (m >> 1) - (i >> 1) : (m >> 1) - (i >> 1) + 1) + 1;
		while(l < r - 1) {
			int mid = l + r >> 1;
			if(check(i, mid)) l = mid; else r = mid;
		}
		if(check(i, l + 1)) l++;
		ans -= l + 1;
		if(ans < 0) ans += MOD;
		if(ans > MOD) ans -= MOD;
	}
	
	printf("%d\n", ans);
	
	return 0;
}
/*
abaabaa
*/