洛谷1050 循环

原题链接

觉得这个大佬写的挺好的就直接复制过来了（略有改动）。

我们可以从尾来分析，即后\(1\)位，后\(2\)位，后\(3\)位，后\(4\)位……后\(k\)位，递推去找。
假使输入数据位\(198123\ 4\)。
1.截取后\(4\)位\(8123\)，只需对\(8123\)做处理。
2.首先取最后一位\(3\)，寻找循环节：\(3,9,7,1\)，循环长度为\(4\)。
3.此时，取后两位\(23\)，而\((23 ^ 4) \mod 100 = 41\)，此时，\(23\)需每次乘以\(41\)，可保证最后一位不变。\(23 \times 41 ^ n\)的循环节为\(43\ 63\ 83\ 3\ 23\)，循环节长度为\(5\)，此时，循环总长度为\(4 \times 5 = 20\)。
4.通过第\(3\)步操作，取后三位\(123\)，\((123 ^ {20}) \mod 1000 = 201\)。\(123 \times 201 ^ n\)的循环节为\(723\ 323\ 923\ 523\ 123\)，循环节长度为\(5\)，此时总长度为\(20 \times 5 = 100\)。
5.还是一样，取后四位\(8123\)，\((8123 ^ {100}) \mod 10000 = 6001\)。\(8123 \times 6001 ^ n\)的循环节为\(6123\ 4123\ 2123\ 123\ 8123\)，循环节长度为\(5\)，此时总长度为\(100 \times 5 = 500\)。

上高精按上述放方法模拟即可。
因为我比较懒，就直接复制了我的高精模板。

#include<cstdio>
#include<cstring>
using namespace std;
typedef long long ll;
const int base = 1e8;
const int N = 1e3 + 10;
int aux[N << 3];
struct bigint {
	int s[N], l;
	void CL() { l = 0; memset(s, 0, sizeof(s)); }
	void pr()
	{
		printf("%d", s[l]);
		for (int i = l - 1; i; i--)
			printf("%08d", s[i]);
	}
	void re_l()
	{
		int i, x = 0, k = 1, L = 0, fl, o;
		char c = getchar();
		for (; c < '0' || c > '9'; c = getchar());
		for (; c >= '0' && c <= '9'; c = getchar())
		{
			if (!(L - 1) && !aux[L])
				L--;
			aux[++L] = c - '0';
		}
		CL();
		l = L / 8 + ((o = L % 8) > 0);
		for (i = 1; i <= o; i++)
			x = x * 10 + aux[i];
		if (o)
			s[l] = x;
		fl = !o ? l + 1 : l;
		for (i = o + 1, x = 0; i <= L; i++, k++)
		{
			x = x * 10 + aux[i];
			if (!(k ^ 8))
			{
				s[--fl] = x;
				x = k = 0;
			}
		}
		if (!l)
			l = 1;
	}
	ll toint()
	{
		ll x = 0;
		for (int i = l; i; i--)
			x = x * base + s[i];
		return x;
	}
	bigint operator = (int b)
	{
		CL();
		do
		{
			s[++l] = b % base;
			b /= base;
		} while (b > 0);
		return *this;
	}
	bigint operator = (ll b)
	{
		CL();
		do
		{
			s[++l] = b % base;
			b /= base;
		} while (b > 0);
		return *this;
	}
	bigint operator + (const int &b)
	{
		bigint c = *this;
		ll x = b;
		for (int i = 1; i <= l && x; i++)
		{
			x = x + c.s[i];
			c.s[i] = x % base;
			x /= base;
		}
		if (x)
			c.s[++c.l] = x;
		return c;
	}
	bigint operator + (const ll &b)
	{
		bigint c = *this;
		ll x = b;
		for (int i = 1; i <= l && x; i++)
		{
			x = x + c.s[i];
			c.s[i] = x % base;
			x /= base;
		}
		if (x)
			c.s[++c.l] = x;
		return c;
	}
	bigint operator + (bigint &b)
	{
		if (b.l < 3)
			return *this + b.toint();
		bigint c;
		ll x = 0;
		int k = l < b.l ? b.l : l;
		c.CL();
		c.l = k;
		for (int i = 1; i <= k; i++)
		{
			x = x + s[i] + b.s[i];
			c.s[i] = x % base;
			x /= base;
		}
		if (x)
			c.s[++c.l] = x;
		return c;
	}
	bigint operator - (const bigint &b)
	{
		bigint c, d = *this;
		ll x = 0;
		c.CL();
		for (int i = 1; i <= l; i++)
		{
			if ((x = d.s[i]) < b.s[i])
			{
				d.s[i + 1]--;
				x += base;
			}
			c.s[i] = x - b.s[i];
		}
		c.l = l;
		for (; !c.s[c.l] && c.l > 1; c.l--);
		return c;
	}
	bigint operator - (const int &b)
	{
		bigint c;
		return *this - (c = b);
	}
	bigint operator - (const ll &b)
	{
		bigint c;
		return *this - (c = b);
	}
	bigint operator * (const int &b)
	{
		bigint c;
		ll x = 0;
		c.CL();
		for (int i = 1; i <= l; i++)
		{
			x = x + 1LL * s[i] * b;
			c.s[i] = x % base;
			x /= base;
		}
		for (c.l = l; x; x /= base)
			c.s[++c.l] = x % base;
		return c;
	}
	bigint operator * (bigint &b)
	{
		if (b.l < 2)
			return *this * b.toint();
		bigint c;
		ll x;
		int i, j, k;
		c.CL();
		for (i = 1; i <= l; i++)
		{
			x = 0;
			for (j = 1; j <= b.l; j++)
			{
				x = x + 1LL * s[i] * b.s[j] + c.s[k = i + j - 1];
				c.s[k] = x % base;
				x /= base;
			}
			if (x)
				c.s[i + b.l] = x;
		}
		for (c.l = l + b.l; !c.s[c.l] && c.l > 1; c.l--);
		return c;
	}
	bigint operator * (const ll &b)
	{
		bigint c;
		if (b > 2e9)
		{
			c = b;
			return *this * c;
		}
		ll x = 0;
		c.CL();
		for (int i = 1; i <= l; i++)
		{
			x = x + b * s[i];
			c.s[i] = x % base;
			x /= base;
		}
		for (c.l = l; x; x /= base)
			c.s[++c.l] = x % base;
		return c;
	}
	bigint operator / (const int &b)
	{
		bigint c;
		ll x = 0;
		c.CL();
		for (int i = l; i; i--)
		{
			c.s[i] = (x * base + s[i]) / b;
			x = (x * base + s[i]) % b;
		}
		for (c.l = l; !c.s[c.l] && c.l > 1; c.l--);
		return c;
	}
	bigint operator / (const ll &b)
	{
		bigint c;
		ll x = 0;
		c.CL();
		for (int i = l; i; i--)
		{
			c.s[i] = (x * base + s[i]) / b;
			x = (x * base + s[i]) % b;
		}
		for (c.l = l; !c.s[c.l] && c.l > 1; c.l--);
		return c;
	}
	bigint operator / (bigint &b)
	{
		if (b.l < 2)
			return *this / b.toint();
		bigint c, d;
		int i, j, le, r, mid, k;
		c.CL();
		d.CL();
		for (i = l; i; i--)
		{
			for (j = ++d.l; j > 1; j--)
				d.s[j] = d.s[j - 1];
			d.s[1] = s[i];
			if (d < b)
				continue;
			le = k = 0;
			r = base - 1;
			while (le <= r)
			{
				mid = (le + r) >> 1;
				if (b * mid <= d)
				{
					le = mid + 1;
					k = mid;
				}
				else
					r = mid - 1;
			}
			c.s[i] = k;
			d = d - b * k;
		}
		for (c.l = l; !c.s[c.l] && c.l > 1; c.l--);
		return c;
	}
	bigint operator % (const int &b)
	{
		bigint c;
		ll x = 0;
		c.CL();
		for (int i = l; i; i--)
			x = (x * base + s[i]) % b;
		return c = x;
	}
	bigint operator % (const ll &b)
	{
		bigint c;
		ll x = 0;
		c.CL();
		for (int i = l; i; i--)
			x = (x * base + s[i]) % b;
		return c = x;
	}
	bigint operator % (bigint &b)
	{
		if (b.l < 2)
			return *this % b.toint();
		bigint c;
		int i, j, le, r, mid, k;
		c.CL();
		for (i = l; i; i--)
		{
			for (j = ++c.l; j > 1; j--)
				c.s[j] = c.s[j - 1];
			c.s[1] = s[i];
			if (c < b)
				continue;
			le = k = 0;
			r = base - 1;
			while (le <= r)
			{
				mid = (le + r) >> 1;
				if (b * mid <= c)
				{
					le = mid + 1;
					k = mid;
				}
				else
					r = mid - 1;
			}
			c = c - b * k;
		}
		for (; !c.s[c.l] && c.l > 1; c.l--);
		return c;
	}
	bigint operator += (bigint &b)
	{
		return *this = *this + b;
	}
	bigint operator += (ll &b)
	{
		return *this = *this + b;
	}
	bigint operator += (int &b)
	{
		return *this = *this + b;
	}
	bigint operator -= (bigint &b)
	{
		return *this = *this - b;
	}
	bigint operator -= (ll &b)
	{
		return *this = *this - b;
	}
	bigint operator -= (int &b)
	{
		return *this = *this - b;
	}
	bigint operator *= (bigint &b)
	{
		return *this = *this * b;
	}
	bigint operator *= (ll &b)
	{
		return *this = *this * b;
	}
	bigint operator *= (int &b)
	{
		return *this = *this * b;
	}
	bigint operator /= (bigint &b)
	{
		return *this = *this / b;
	}
	bigint operator /= (ll &b)
	{
		return *this = *this / b;
	}
	bigint operator /= (int &b)
	{
		return *this = *this / b;
	}
	bigint operator %= (bigint &b)
	{
		return *this = *this % b;
	}
	bigint operator %= (ll &b)
	{
		return *this = *this % b;
	}
	bigint operator %= (int &b)
	{
		return *this = *this % b;
	}
	bool operator < (const bigint &b) const
	{
		if (l ^ b.l)
			return l < b.l;
		for (int i = l; i; i--)
			if (s[i] ^ b.s[i])
				return s[i] < b.s[i];
		return false;
	}
	bool operator <= (const bigint &b) const
	{
		if (l ^ b.l)
			return l < b.l;
		for (int i = l; i; i--)
			if (s[i] ^ b.s[i])
				return s[i] < b.s[i];
		return true;
	}
	bool operator > (const bigint &b) const
	{
		if (l ^ b.l)
			return l > b.l;
		for (int i = l; i; i--)
			if (s[i] ^ b.s[i])
				return s[i] > b.s[i];
		return false;
	}
	bool operator >= (const bigint &b) const
	{
		if (l ^ b.l)
			return l > b.l;
		for (int i = l; i; i--)
			if (s[i] ^ b.s[i])
				return s[i] > b.s[i];
		return true;
	}
	bool operator == (const bigint &b) const
	{
		if (l ^ b.l)
			return false;
		for (int i = l; i; i--)
			if (s[i] ^ b.s[i])
				return false;
		return true;
	}
	bool operator != (const bigint &b) const
	{
		if (l ^ b.l)
			return true;
		for (int i = l; i; i--)
			if (s[i] ^ b.s[i])
				return true;
		return false;
	}
	bool operator < (ll b) const
	{
		bigint c;
		return *this < (c = b);
	}
	bool operator <= (ll b) const
	{
		bigint c;
		return *this <= (c = b);
	}
	bool operator > (ll b) const
	{
		bigint c;
		return *this > (c = b);
	}
	bool operator >= (ll b) const
	{
		bigint c;
		return *this >= (c = b);
	}
	bool operator == (ll b) const
	{
		bigint c;
		return *this == (c = b);
	}
	bool operator != (ll b) const
	{
		bigint c;
		return *this != (c = b);
	}
	bool operator < (int b) const
	{
		bigint c;
		return *this < (c = b);
	}
	bool operator <= (int b) const
	{
		bigint c;
		return *this <= (c = b);
	}
	bool operator > (int b) const
	{
		bigint c;
		return *this > (c = b);
	}
	bool operator >= (int b) const
	{
		bigint c;
		return *this >= (c = b);
	}
	bool operator == (int b) const
	{
		bigint c;
		return *this == (c = b);
	}
	bool operator != (int b) const
	{
		bigint c;
		return *this != (c = b);
	}
};
bigint n, an, mod[N], la, nw, m;
bigint ksm(bigint x, bigint y, bigint md)
{
	bigint s;
	s = 1;
	for (; y > 0; y = y / 2, x = x * x % md)
		if (y.s[1] & 1)
			s = s * x % md;
	return s;
}
int main()
{
	int i, j, k;
	n.re_l(); scanf("%d", &k);
	for (mod[1] = 10, i = 2; i <= k; i++)
		mod[i] = mod[i - 1] * 10;
	n %= mod[k];
	for (an = 1, i = 1; i <= k; i++)
	{
		nw = n % mod[i];
		m = ksm(nw, an, mod[i]);
		i ^ 1 ? la = nw = nw * m % mod[i] : la = nw;
		for (j = 2; j < 12; j++)
		{
			nw = nw * m % mod[i];
			if (nw == la)
				break;
		}
		if (j > 11)
		{
			printf("-1");
			return 0;
		}
		an = an * (j - 1);
	}
	an.pr();
	return 0;
}