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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Blake is a CEO of a large company called "Blake Technologies". He loves his company very much and he thinks that his company should be the best. That is why every candidate needs to pass through the interview that consists of the following problem. We define function f(x, l, r) as a bitwise OR of integers xl, xl + 1, ..., xr, where xi is the i-th element of the array x. You are given two arrays a and b of length n. You need to determine the maximum value of sum f(a, l, r) + f(b, l, r) among all possible 1 ≤ l ≤ r ≤ n. <image> Input The first line of the input contains a single integer n (1 ≤ n ≤ 1000) — the length of the arrays. The second line contains n integers ai (0 ≤ ai ≤ 109). The third line contains n integers bi (0 ≤ bi ≤ 109). Output Print a single integer — the maximum value of sum f(a, l, r) + f(b, l, r) among all possible 1 ≤ l ≤ r ≤ n. Examples Input 5 1 2 4 3 2 2 3 3 12 1 Output 22 Input 10 13 2 7 11 8 4 9 8 5 1 5 7 18 9 2 3 0 11 8 6 Output 46 Note Bitwise OR of two non-negative integers a and b is the number c = a OR b, such that each of its digits in binary notation is 1 if and only if at least one of a or b have 1 in the corresponding position in binary notation. In the first sample, one of the optimal answers is l = 2 and r = 4, because f(a, 2, 4) + f(b, 2, 4) = (2 OR 4 OR 3) + (3 OR 3 OR 12) = 7 + 15 = 22. Other ways to get maximum value is to choose l = 1 and r = 4, l = 1 and r = 5, l = 2 and r = 4, l = 2 and r = 5, l = 3 and r = 4, or l = 3 and r = 5. In the second sample, the maximum value is obtained for l = 1 and r = 9. Submitted Solution: ``` n=int(input()) a=list(map(int,input().split())) b=list(map(int,input().split())) m=0 for l in range(n): x=a[l] y=b[l] for r in range(l,n): x=x|a[r] y=y|b[r] m=max(m,x+y) print(m) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Blake is a CEO of a large company called "Blake Technologies". He loves his company very much and he thinks that his company should be the best. That is why every candidate needs to pass through the interview that consists of the following problem. We define function f(x, l, r) as a bitwise OR of integers xl, xl + 1, ..., xr, where xi is the i-th element of the array x. You are given two arrays a and b of length n. You need to determine the maximum value of sum f(a, l, r) + f(b, l, r) among all possible 1 ≤ l ≤ r ≤ n. <image> Input The first line of the input contains a single integer n (1 ≤ n ≤ 1000) — the length of the arrays. The second line contains n integers ai (0 ≤ ai ≤ 109). The third line contains n integers bi (0 ≤ bi ≤ 109). Output Print a single integer — the maximum value of sum f(a, l, r) + f(b, l, r) among all possible 1 ≤ l ≤ r ≤ n. Examples Input 5 1 2 4 3 2 2 3 3 12 1 Output 22 Input 10 13 2 7 11 8 4 9 8 5 1 5 7 18 9 2 3 0 11 8 6 Output 46 Note Bitwise OR of two non-negative integers a and b is the number c = a OR b, such that each of its digits in binary notation is 1 if and only if at least one of a or b have 1 in the corresponding position in binary notation. In the first sample, one of the optimal answers is l = 2 and r = 4, because f(a, 2, 4) + f(b, 2, 4) = (2 OR 4 OR 3) + (3 OR 3 OR 12) = 7 + 15 = 22. Other ways to get maximum value is to choose l = 1 and r = 4, l = 1 and r = 5, l = 2 and r = 4, l = 2 and r = 5, l = 3 and r = 4, or l = 3 and r = 5. In the second sample, the maximum value is obtained for l = 1 and r = 9. Submitted Solution: ``` if __name__ == '__main__': n = int(input()) a = map(int, input().split()) b = map(int, input().split()) va = vb = 0 for i in a: va |= i for i in b: vb |= i print(va + vb) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Blake is a CEO of a large company called "Blake Technologies". He loves his company very much and he thinks that his company should be the best. That is why every candidate needs to pass through the interview that consists of the following problem. We define function f(x, l, r) as a bitwise OR of integers xl, xl + 1, ..., xr, where xi is the i-th element of the array x. You are given two arrays a and b of length n. You need to determine the maximum value of sum f(a, l, r) + f(b, l, r) among all possible 1 ≤ l ≤ r ≤ n. <image> Input The first line of the input contains a single integer n (1 ≤ n ≤ 1000) — the length of the arrays. The second line contains n integers ai (0 ≤ ai ≤ 109). The third line contains n integers bi (0 ≤ bi ≤ 109). Output Print a single integer — the maximum value of sum f(a, l, r) + f(b, l, r) among all possible 1 ≤ l ≤ r ≤ n. Examples Input 5 1 2 4 3 2 2 3 3 12 1 Output 22 Input 10 13 2 7 11 8 4 9 8 5 1 5 7 18 9 2 3 0 11 8 6 Output 46 Note Bitwise OR of two non-negative integers a and b is the number c = a OR b, such that each of its digits in binary notation is 1 if and only if at least one of a or b have 1 in the corresponding position in binary notation. In the first sample, one of the optimal answers is l = 2 and r = 4, because f(a, 2, 4) + f(b, 2, 4) = (2 OR 4 OR 3) + (3 OR 3 OR 12) = 7 + 15 = 22. Other ways to get maximum value is to choose l = 1 and r = 4, l = 1 and r = 5, l = 2 and r = 4, l = 2 and r = 5, l = 3 and r = 4, or l = 3 and r = 5. In the second sample, the maximum value is obtained for l = 1 and r = 9. Submitted Solution: ``` from functools import reduce; input() a = reduce(lambda x, y: int(x) | int(y), input().split()) b = reduce(lambda x, y: int(x) | int(y), input().split()) print(a + b) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Blake is a CEO of a large company called "Blake Technologies". He loves his company very much and he thinks that his company should be the best. That is why every candidate needs to pass through the interview that consists of the following problem. We define function f(x, l, r) as a bitwise OR of integers xl, xl + 1, ..., xr, where xi is the i-th element of the array x. You are given two arrays a and b of length n. You need to determine the maximum value of sum f(a, l, r) + f(b, l, r) among all possible 1 ≤ l ≤ r ≤ n. <image> Input The first line of the input contains a single integer n (1 ≤ n ≤ 1000) — the length of the arrays. The second line contains n integers ai (0 ≤ ai ≤ 109). The third line contains n integers bi (0 ≤ bi ≤ 109). Output Print a single integer — the maximum value of sum f(a, l, r) + f(b, l, r) among all possible 1 ≤ l ≤ r ≤ n. Examples Input 5 1 2 4 3 2 2 3 3 12 1 Output 22 Input 10 13 2 7 11 8 4 9 8 5 1 5 7 18 9 2 3 0 11 8 6 Output 46 Note Bitwise OR of two non-negative integers a and b is the number c = a OR b, such that each of its digits in binary notation is 1 if and only if at least one of a or b have 1 in the corresponding position in binary notation. In the first sample, one of the optimal answers is l = 2 and r = 4, because f(a, 2, 4) + f(b, 2, 4) = (2 OR 4 OR 3) + (3 OR 3 OR 12) = 7 + 15 = 22. Other ways to get maximum value is to choose l = 1 and r = 4, l = 1 and r = 5, l = 2 and r = 4, l = 2 and r = 5, l = 3 and r = 4, or l = 3 and r = 5. In the second sample, the maximum value is obtained for l = 1 and r = 9. Submitted Solution: ``` n = int(input()) n1 = input().split(' ') n2 = input().split(' ') sum1 = int(n1[0]) | int(n1[1]) | int(n1[2]) | int(n1[3]) | int(n1[4]) sum2 = int(n2[0]) | int(n2[1]) | int(n2[2]) | int(n2[3]) | int(n2[4]) print(sum1 + sum2) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Blake is a CEO of a large company called "Blake Technologies". He loves his company very much and he thinks that his company should be the best. That is why every candidate needs to pass through the interview that consists of the following problem. We define function f(x, l, r) as a bitwise OR of integers xl, xl + 1, ..., xr, where xi is the i-th element of the array x. You are given two arrays a and b of length n. You need to determine the maximum value of sum f(a, l, r) + f(b, l, r) among all possible 1 ≤ l ≤ r ≤ n. <image> Input The first line of the input contains a single integer n (1 ≤ n ≤ 1000) — the length of the arrays. The second line contains n integers ai (0 ≤ ai ≤ 109). The third line contains n integers bi (0 ≤ bi ≤ 109). Output Print a single integer — the maximum value of sum f(a, l, r) + f(b, l, r) among all possible 1 ≤ l ≤ r ≤ n. Examples Input 5 1 2 4 3 2 2 3 3 12 1 Output 22 Input 10 13 2 7 11 8 4 9 8 5 1 5 7 18 9 2 3 0 11 8 6 Output 46 Note Bitwise OR of two non-negative integers a and b is the number c = a OR b, such that each of its digits in binary notation is 1 if and only if at least one of a or b have 1 in the corresponding position in binary notation. In the first sample, one of the optimal answers is l = 2 and r = 4, because f(a, 2, 4) + f(b, 2, 4) = (2 OR 4 OR 3) + (3 OR 3 OR 12) = 7 + 15 = 22. Other ways to get maximum value is to choose l = 1 and r = 4, l = 1 and r = 5, l = 2 and r = 4, l = 2 and r = 5, l = 3 and r = 4, or l = 3 and r = 5. In the second sample, the maximum value is obtained for l = 1 and r = 9. Submitted Solution: ``` from functools import reduce def solve(n,a,b): l = 0 r = l+3 max_val = 0 for i in range(n-2): val = reduce(lambda x,y: x | y , a[l:r])+reduce(lambda x,y: x | y , b[l:r]) if val > max_val: max_val = val l = i+1 r = l+3 return max_val def main() : # na,nb = list(map(int, input().split(' '))) # k,m = list(map(int, input().split(' '))) # a = list(map(int, input().split(' '))) # b = list(map(int, input().split(' '))) # s = input() # res='' # n = int(input()) # arr = [] # for _ in range(n): # i = list(map(int, input().split(' '))) # arr.append(i) # # for i in arr: n = int(input()) a = list(map(int, input().split(' '))) b = list(map(int, input().split(' '))) # s = input() print(solve(n,a,b)) main() ```
instruction
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Blake is a CEO of a large company called "Blake Technologies". He loves his company very much and he thinks that his company should be the best. That is why every candidate needs to pass through the interview that consists of the following problem. We define function f(x, l, r) as a bitwise OR of integers xl, xl + 1, ..., xr, where xi is the i-th element of the array x. You are given two arrays a and b of length n. You need to determine the maximum value of sum f(a, l, r) + f(b, l, r) among all possible 1 ≤ l ≤ r ≤ n. <image> Input The first line of the input contains a single integer n (1 ≤ n ≤ 1000) — the length of the arrays. The second line contains n integers ai (0 ≤ ai ≤ 109). The third line contains n integers bi (0 ≤ bi ≤ 109). Output Print a single integer — the maximum value of sum f(a, l, r) + f(b, l, r) among all possible 1 ≤ l ≤ r ≤ n. Examples Input 5 1 2 4 3 2 2 3 3 12 1 Output 22 Input 10 13 2 7 11 8 4 9 8 5 1 5 7 18 9 2 3 0 11 8 6 Output 46 Note Bitwise OR of two non-negative integers a and b is the number c = a OR b, such that each of its digits in binary notation is 1 if and only if at least one of a or b have 1 in the corresponding position in binary notation. In the first sample, one of the optimal answers is l = 2 and r = 4, because f(a, 2, 4) + f(b, 2, 4) = (2 OR 4 OR 3) + (3 OR 3 OR 12) = 7 + 15 = 22. Other ways to get maximum value is to choose l = 1 and r = 4, l = 1 and r = 5, l = 2 and r = 4, l = 2 and r = 5, l = 3 and r = 4, or l = 3 and r = 5. In the second sample, the maximum value is obtained for l = 1 and r = 9. Submitted Solution: ``` n = int(input()) lst1 = list(map(int, input().split())) lst2 = list(map(int, input().split())) ans = -1 for i in range(n): s = lst1[i] s1 = lst2[i] ans = max(ans, s + s1) for j in range(i + 1, n): s = s | lst1[j] s1 = s | lst2[j] ans = max(ans, s + s1) print(ans) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a set of integer numbers, initially it is empty. You should perform n queries. There are three different types of queries: * 1 l r — Add all missing numbers from the interval [l, r] * 2 l r — Remove all present numbers from the interval [l, r] * 3 l r — Invert the interval [l, r] — add all missing and remove all present numbers from the interval [l, r] After each query you should output MEX of the set — the smallest positive (MEX ≥ 1) integer number which is not presented in the set. Input The first line contains one integer number n (1 ≤ n ≤ 105). Next n lines contain three integer numbers t, l, r (1 ≤ t ≤ 3, 1 ≤ l ≤ r ≤ 1018) — type of the query, left and right bounds. Output Print MEX of the set after each query. Examples Input 3 1 3 4 3 1 6 2 1 3 Output 1 3 1 Input 4 1 1 3 3 5 6 2 4 4 3 1 6 Output 4 4 4 1 Note Here are contents of the set after each query in the first example: 1. {3, 4} — the interval [3, 4] is added 2. {1, 2, 5, 6} — numbers {3, 4} from the interval [1, 6] got deleted and all the others are added 3. {5, 6} — numbers {1, 2} got deleted Submitted Solution: ``` try: n = int(input()) coms = [tuple(map(int, input().split())) for _ in range(0, n)] nums = set() for com in coms: tmp = set(range(com[1], com[2] + 1)) if com[0] == 1: nums |= tmp elif com[0] == 2: nums -= tmp else: nums ^= tmp tmp = set(range(1, max(tmp) + 2)) - nums print(min(tmp)) except Exception as e: print(e) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a set of integer numbers, initially it is empty. You should perform n queries. There are three different types of queries: * 1 l r — Add all missing numbers from the interval [l, r] * 2 l r — Remove all present numbers from the interval [l, r] * 3 l r — Invert the interval [l, r] — add all missing and remove all present numbers from the interval [l, r] After each query you should output MEX of the set — the smallest positive (MEX ≥ 1) integer number which is not presented in the set. Input The first line contains one integer number n (1 ≤ n ≤ 105). Next n lines contain three integer numbers t, l, r (1 ≤ t ≤ 3, 1 ≤ l ≤ r ≤ 1018) — type of the query, left and right bounds. Output Print MEX of the set after each query. Examples Input 3 1 3 4 3 1 6 2 1 3 Output 1 3 1 Input 4 1 1 3 3 5 6 2 4 4 3 1 6 Output 4 4 4 1 Note Here are contents of the set after each query in the first example: 1. {3, 4} — the interval [3, 4] is added 2. {1, 2, 5, 6} — numbers {3, 4} from the interval [1, 6] got deleted and all the others are added 3. {5, 6} — numbers {1, 2} got deleted Submitted Solution: ``` r=[] def b1 (b) : global r for i in range (b[1],b[2]+1) : r.append(i) t=1 while 2>1 : if t not in r : print(t) break t=t+1 def b2 (b) : global r for i in range(b[1],b[2]+1) : if i in r: e=r.index(i) del r[e] t=1 while 2>1 : if t not in r : print(t) break t=t+1 def b3 (b) : global r for i in range(b[1],b[2]+1) : if i in r: e=r.index(i) del r[e] else : r.append(i) t=1 while 2>1 : if t not in r : print(t) break t=t+1 a=int(input()) h=[] for i in range (a) : h.append(list(map(int, input().split()))) for i in range (a) : if h[i][0]==1 : b1(h[i]) elif h[i][0]==2 : b2(h[i]) elif h[i][0]==3 : b3(h[i]) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a set of integer numbers, initially it is empty. You should perform n queries. There are three different types of queries: * 1 l r — Add all missing numbers from the interval [l, r] * 2 l r — Remove all present numbers from the interval [l, r] * 3 l r — Invert the interval [l, r] — add all missing and remove all present numbers from the interval [l, r] After each query you should output MEX of the set — the smallest positive (MEX ≥ 1) integer number which is not presented in the set. Input The first line contains one integer number n (1 ≤ n ≤ 105). Next n lines contain three integer numbers t, l, r (1 ≤ t ≤ 3, 1 ≤ l ≤ r ≤ 1018) — type of the query, left and right bounds. Output Print MEX of the set after each query. Examples Input 3 1 3 4 3 1 6 2 1 3 Output 1 3 1 Input 4 1 1 3 3 5 6 2 4 4 3 1 6 Output 4 4 4 1 Note Here are contents of the set after each query in the first example: 1. {3, 4} — the interval [3, 4] is added 2. {1, 2, 5, 6} — numbers {3, 4} from the interval [1, 6] got deleted and all the others are added 3. {5, 6} — numbers {1, 2} got deleted Submitted Solution: ``` n = int(input()) coms = [tuple(map(int, input().split())) for _ in range(0, n)] nums = set() for com in coms: tmp = set(range(com[1], com[2] + 1)) if com[0] == 1: nums |= tmp elif com[0] == 2: nums -= tmp else: nums ^= tmp tmp = set(range(1, max(tmp) + 2)) - nums print(min(tmp) if tmp else 1) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a set of integer numbers, initially it is empty. You should perform n queries. There are three different types of queries: * 1 l r — Add all missing numbers from the interval [l, r] * 2 l r — Remove all present numbers from the interval [l, r] * 3 l r — Invert the interval [l, r] — add all missing and remove all present numbers from the interval [l, r] After each query you should output MEX of the set — the smallest positive (MEX ≥ 1) integer number which is not presented in the set. Input The first line contains one integer number n (1 ≤ n ≤ 105). Next n lines contain three integer numbers t, l, r (1 ≤ t ≤ 3, 1 ≤ l ≤ r ≤ 1018) — type of the query, left and right bounds. Output Print MEX of the set after each query. Examples Input 3 1 3 4 3 1 6 2 1 3 Output 1 3 1 Input 4 1 1 3 3 5 6 2 4 4 3 1 6 Output 4 4 4 1 Note Here are contents of the set after each query in the first example: 1. {3, 4} — the interval [3, 4] is added 2. {1, 2, 5, 6} — numbers {3, 4} from the interval [1, 6] got deleted and all the others are added 3. {5, 6} — numbers {1, 2} got deleted Submitted Solution: ``` #MAXN = 8 MAXN = 524288 command = [] left = [] right = [] save1 = [] class Lazy: min_blank = 0 min_filled = MAXN+1 upd = 0 Ltree = [] def init(ind,f1,l1): Ltree[ind].min_blank = f1 #print(ind, f1, l1, Ltree[ind].min_blank) if(f1 == l1): return 0 init(ind*2,f1,(f1+l1)//2) init(ind*2+1,(f1+l1)//2+1,l1) def upd(ind,f1,l1,f2,l2,key): if(save1[f1] > l2 or save1[l1] < f2): return 0 mi = (f1+l1)//2 #print(ind,f1,l1,f2,l2,key) if(Ltree[ind].upd != 0 and f1 != l1): process(2*ind,f1,Ltree[ind].upd) process(2*ind+1,f1,Ltree[ind].upd) Ltree[ind].upd = 0 if(save1[f1] >= f2 and save1[l1] <= l2): process(ind,f1,key) Ltree[ind].upd = 0 return 0 elif(f1 != l1): upd(ind*2,f1,mi,f2,l2,key) upd(ind*2+1,mi+1,l1,f2,l2,key) Ltree[ind].min_blank = min(Ltree[2*ind].min_blank,Ltree[2*ind+1].min_blank) Ltree[ind].min_filled = min(Ltree[2*ind].min_filled,Ltree[2*ind+1].min_filled) #print("!!!!",ind,f1,l1,f2,l2, " : ", Ltree[ind].min_blank,Ltree[ind].min_filled," ; ",Ltree[ind].upd) def process(ind,f1,key): if(key == 1): Ltree[ind].min_blank = MAXN+1 Ltree[ind].min_filled = f1 Ltree[ind].upd = key elif(key == 2): Ltree[ind].min_blank = f1 Ltree[ind].min_filled = MAXN+1 Ltree[ind].upd = key elif(key == 3): Ltree[ind].min_blank, Ltree[ind].min_filled = Ltree[ind].min_filled, Ltree[ind].min_blank Ltree[ind].upd = key^Ltree[ind].upd def main(): n = int(input().split()[0]) for i in range(MAXN*2): Ltree.append(Lazy()) init(1,1,MAXN) global save1 save2 = [] command = [0]*n left = [0]*n right = [0]*n for i in range(n): command[i], left[i], right[i] = map(int,input().split()) save2.append(left[i]) save2.append(right[i]) save2.append(right[i]+1) #upd(1,1,MAXN,l,r,command) #print(Ltree[1].min_blank) save2.append(0) save2.append(1) save2.sort() lenSave2 = len(save2) for i in range(lenSave2): if(i == 0 or save2[i] != save2[i-1]): save1.append(save2[i]) save1 = list(set(save1)) tmp2 = save1[-1] tmp3 = len(save1) for i in range(MAXN-tmp3+1): save1.append(tmp2+3) #print(save1) for i in range(n): upd(1,1,MAXN,left[i],right[i],command[i]) print(save1[Ltree[1].min_blank]) if __name__ == "__main__": main() ```
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Provide a correct Python 3 solution for this coding contest problem. This is an output-only problem. You shouldn't read anything from the input. In short, your task is to simulate multiplication by using only comparison (x < y) and addition (x + y). There is no input in this problem, you just print a sequence of operations. Imagine that there is a big array a[0], a[1], ..., a[N-1] of length N. The first two values are initially two non-negative integers A and B (which are unknown to you), the other elements are zeros. Your goal is to get the product A \cdot B in a[2] at the end. You are allowed operations of two types, with the following format (where 0 \leq i, j, k < N): * `+ i j k` — applies operation a[k] = a[i] + a[j]. * `< i j k` — applies operation a[k] = a[i] < a[j]. That is, if a[i] < a[j] then a[k] becomes 1, otherwise it becomes 0. You can use at most Q operations. Elements of a can't exceed V. Indices (i, j, k) don't have to be distinct. It's allowed to modify any element of the array (including the first two). The actual checker simulates the process for multiple pairs (A, B) within a single test. Each time, the checker chooses values A and B, creates the array a = [A, B, 0, 0, \ldots, 0], applies all your operations and ensures that a[2] = A \cdot B. Constraints * 0 \leq A, B \leq 10^9 * N = Q = 200\,000 * V = 10^{19} = 10\,000\,000\,000\,000\,000\,000 Input The Standard Input is empty. Output In the first line, print the number of operations. Each operation should then be printed in a single line of format `+ i j k` or `< i j k`. Example Input Output
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"Correct Solution: ``` n=97 def c(i,j,k):print('<',i,j,k) def a(i,j,k):print('+',i,j,k) def d(x,i,j): for t in range(30): a(j+t-1,j+t-1,j+t) a(j+t,n,j+t) for s in range(j+t,j+29):a(s,s,s+1) c(j+29,x,i+t) a(j+t-1,j+t-1,j+t) a(j+t,i+t,j+t) print(3933) a(0,1,n) c(2,n,n) a(0,n,3) a(1,n,4) d(3,5,36) d(4,36,67) for t in range(59): a(2,2,2) for s in range(t+1): if t-30<s<30:a(5+t-s,36+s,98);c(n,98,99);a(2,99,2) ```
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5
213,539
Provide a correct Python 3 solution for this coding contest problem. This is an output-only problem. You shouldn't read anything from the input. In short, your task is to simulate multiplication by using only comparison (x < y) and addition (x + y). There is no input in this problem, you just print a sequence of operations. Imagine that there is a big array a[0], a[1], ..., a[N-1] of length N. The first two values are initially two non-negative integers A and B (which are unknown to you), the other elements are zeros. Your goal is to get the product A \cdot B in a[2] at the end. You are allowed operations of two types, with the following format (where 0 \leq i, j, k < N): * `+ i j k` — applies operation a[k] = a[i] + a[j]. * `< i j k` — applies operation a[k] = a[i] < a[j]. That is, if a[i] < a[j] then a[k] becomes 1, otherwise it becomes 0. You can use at most Q operations. Elements of a can't exceed V. Indices (i, j, k) don't have to be distinct. It's allowed to modify any element of the array (including the first two). The actual checker simulates the process for multiple pairs (A, B) within a single test. Each time, the checker chooses values A and B, creates the array a = [A, B, 0, 0, \ldots, 0], applies all your operations and ensures that a[2] = A \cdot B. Constraints * 0 \leq A, B \leq 10^9 * N = Q = 200\,000 * V = 10^{19} = 10\,000\,000\,000\,000\,000\,000 Input The Standard Input is empty. Output In the first line, print the number of operations. Each operation should then be printed in a single line of format `+ i j k` or `< i j k`. Example Input Output
instruction
0
106,770
5
213,540
"Correct Solution: ``` n=97 p=print r=range def c(i,j,k):p('<',i,j,k) def a(i,j,k=0):p('+',i,j,max(i,k)) def b(i):a(i,i,i+1) def d(x,i,j): for t in r(30): b(j+t-1);a(j+t,n) for s in r(j+t,j+29):b(s) c(j+29,x,i+t);b(j+t-1);a(j+t,i+t) p(3933) a(0,1,n) c(2,n,n) a(0,n,3) a(1,n,4) d(3,5,36) d(4,36,67) for t in r(59): a(2,2) for s in r(t+1): if t-30<s<30:a(5+t-s,36+s,98);c(n,98,99);a(2,99) ```
output
1
106,770
5
213,541
Provide a correct Python 3 solution for this coding contest problem. This is an output-only problem. You shouldn't read anything from the input. In short, your task is to simulate multiplication by using only comparison (x < y) and addition (x + y). There is no input in this problem, you just print a sequence of operations. Imagine that there is a big array a[0], a[1], ..., a[N-1] of length N. The first two values are initially two non-negative integers A and B (which are unknown to you), the other elements are zeros. Your goal is to get the product A \cdot B in a[2] at the end. You are allowed operations of two types, with the following format (where 0 \leq i, j, k < N): * `+ i j k` — applies operation a[k] = a[i] + a[j]. * `< i j k` — applies operation a[k] = a[i] < a[j]. That is, if a[i] < a[j] then a[k] becomes 1, otherwise it becomes 0. You can use at most Q operations. Elements of a can't exceed V. Indices (i, j, k) don't have to be distinct. It's allowed to modify any element of the array (including the first two). The actual checker simulates the process for multiple pairs (A, B) within a single test. Each time, the checker chooses values A and B, creates the array a = [A, B, 0, 0, \ldots, 0], applies all your operations and ensures that a[2] = A \cdot B. Constraints * 0 \leq A, B \leq 10^9 * N = Q = 200\,000 * V = 10^{19} = 10\,000\,000\,000\,000\,000\,000 Input The Standard Input is empty. Output In the first line, print the number of operations. Each operation should then be printed in a single line of format `+ i j k` or `< i j k`. Example Input Output
instruction
0
106,771
5
213,542
"Correct Solution: ``` n=97 def c(i,j,k):print('<',i,j,k) def a(i,j,k):print('+',i,j,k) def m(i,j,k): for t in range(59): a(k,k,k) for s in range(t+1): if t-30<s<30:a(i+t-s,j+s,98);c(n,98,99);a(k,99,k) def d(x,i,j): for t in range(30): a(j+t-1,j+t-1,j+t) a(j+t,n,j+t) for s in range(j+t,j+29):a(s,s,s+1) c(j+29,x,i+t) a(j+t-1,j+t-1,j+t) a(j+t,i+t,j+t) print(3933) a(0,1,n) c(2,n,n) a(0,n,3) a(1,n,4) d(3,5,36) d(4,36,67) m(5,36,2) ```
output
1
106,771
5
213,543
Provide a correct Python 3 solution for this coding contest problem. This is an output-only problem. You shouldn't read anything from the input. In short, your task is to simulate multiplication by using only comparison (x < y) and addition (x + y). There is no input in this problem, you just print a sequence of operations. Imagine that there is a big array a[0], a[1], ..., a[N-1] of length N. The first two values are initially two non-negative integers A and B (which are unknown to you), the other elements are zeros. Your goal is to get the product A \cdot B in a[2] at the end. You are allowed operations of two types, with the following format (where 0 \leq i, j, k < N): * `+ i j k` — applies operation a[k] = a[i] + a[j]. * `< i j k` — applies operation a[k] = a[i] < a[j]. That is, if a[i] < a[j] then a[k] becomes 1, otherwise it becomes 0. You can use at most Q operations. Elements of a can't exceed V. Indices (i, j, k) don't have to be distinct. It's allowed to modify any element of the array (including the first two). The actual checker simulates the process for multiple pairs (A, B) within a single test. Each time, the checker chooses values A and B, creates the array a = [A, B, 0, 0, \ldots, 0], applies all your operations and ensures that a[2] = A \cdot B. Constraints * 0 \leq A, B \leq 10^9 * N = Q = 200\,000 * V = 10^{19} = 10\,000\,000\,000\,000\,000\,000 Input The Standard Input is empty. Output In the first line, print the number of operations. Each operation should then be printed in a single line of format `+ i j k` or `< i j k`. Example Input Output
instruction
0
106,772
5
213,544
"Correct Solution: ``` n=97 p=print r=range def c(i,j,k):p('<',i,j,k) def a(i,j,k=0):p('+',i,j,max(i,k)) def b(i):a(i,i,i+1) def d(x,i,j): for t in r(30): b(j+t-1) a(j+t,n) for s in r(j+t,j+29):b(s) c(j+29,x,i+t) b(j+t-1) a(j+t,i+t) p(3933) a(0,1,n) c(2,n,n) a(0,n,3) a(1,n,4) d(3,5,36) d(4,36,67) for t in r(59): a(2,2) for s in r(t+1): if t-30<s<30:a(5+t-s,36+s,98);c(n,98,99);a(2,99) ```
output
1
106,772
5
213,545
Provide a correct Python 3 solution for this coding contest problem. This is an output-only problem. You shouldn't read anything from the input. In short, your task is to simulate multiplication by using only comparison (x < y) and addition (x + y). There is no input in this problem, you just print a sequence of operations. Imagine that there is a big array a[0], a[1], ..., a[N-1] of length N. The first two values are initially two non-negative integers A and B (which are unknown to you), the other elements are zeros. Your goal is to get the product A \cdot B in a[2] at the end. You are allowed operations of two types, with the following format (where 0 \leq i, j, k < N): * `+ i j k` — applies operation a[k] = a[i] + a[j]. * `< i j k` — applies operation a[k] = a[i] < a[j]. That is, if a[i] < a[j] then a[k] becomes 1, otherwise it becomes 0. You can use at most Q operations. Elements of a can't exceed V. Indices (i, j, k) don't have to be distinct. It's allowed to modify any element of the array (including the first two). The actual checker simulates the process for multiple pairs (A, B) within a single test. Each time, the checker chooses values A and B, creates the array a = [A, B, 0, 0, \ldots, 0], applies all your operations and ensures that a[2] = A \cdot B. Constraints * 0 \leq A, B \leq 10^9 * N = Q = 200\,000 * V = 10^{19} = 10\,000\,000\,000\,000\,000\,000 Input The Standard Input is empty. Output In the first line, print the number of operations. Each operation should then be printed in a single line of format `+ i j k` or `< i j k`. Example Input Output
instruction
0
106,773
5
213,546
"Correct Solution: ``` n = q = 2*10**5 fla = [] def pri(s): fla.append(s) pri("+ 0 1 5") pri("< 3 5 4") max_log = 30 pri("+ 0 4 0") pri("+ 1 4 1") for i in reversed(range(max_log)): pri("+ 3 4 8") for _ in range(i): pri("+ 8 8 8") pri("+ 6 8 9") pri("< 9 0 %d" % (100+i)) pri("+ %d 3 9" % (100+i)) for _ in range(i): pri("+ 9 9 9") pri("+ 6 9 6") for i in reversed(range(max_log)): pri("+ 3 4 8") for _ in range(i): pri("+ 8 8 8") pri("+ 7 8 9") pri("< 9 1 %d" % (200+i)) pri("+ %d 3 9" % (200+i)) for _ in range(i): pri("+ 9 9 9") pri("+ 7 9 7") def an(i, j, k): pri("+ %d %d 6" % (i, j)) pri("< %d %d 7" % (i, j)) pri("< %d %d 8" % (j, i)) pri("+ 7 8 7") pri("< 7 6 %d" % k) for i in range(max_log): for j in range(max_log): an(100+i, 200+j, 6) pri("+ %d 6 %d" % (i+j+300, i+j+300)) for i in range(max_log*2): for _ in range(i): pri("+ %d %d %d" % (300+i, 300+i, 300+i)) pri("+ %d 2 2" % (300+i)) print(len(fla)) print("\n".join(fla)) ```
output
1
106,773
5
213,547
Provide a correct Python 3 solution for this coding contest problem. This is an output-only problem. You shouldn't read anything from the input. In short, your task is to simulate multiplication by using only comparison (x < y) and addition (x + y). There is no input in this problem, you just print a sequence of operations. Imagine that there is a big array a[0], a[1], ..., a[N-1] of length N. The first two values are initially two non-negative integers A and B (which are unknown to you), the other elements are zeros. Your goal is to get the product A \cdot B in a[2] at the end. You are allowed operations of two types, with the following format (where 0 \leq i, j, k < N): * `+ i j k` — applies operation a[k] = a[i] + a[j]. * `< i j k` — applies operation a[k] = a[i] < a[j]. That is, if a[i] < a[j] then a[k] becomes 1, otherwise it becomes 0. You can use at most Q operations. Elements of a can't exceed V. Indices (i, j, k) don't have to be distinct. It's allowed to modify any element of the array (including the first two). The actual checker simulates the process for multiple pairs (A, B) within a single test. Each time, the checker chooses values A and B, creates the array a = [A, B, 0, 0, \ldots, 0], applies all your operations and ensures that a[2] = A \cdot B. Constraints * 0 \leq A, B \leq 10^9 * N = Q = 200\,000 * V = 10^{19} = 10\,000\,000\,000\,000\,000\,000 Input The Standard Input is empty. Output In the first line, print the number of operations. Each operation should then be printed in a single line of format `+ i j k` or `< i j k`. Example Input Output
instruction
0
106,774
5
213,548
"Correct Solution: ``` n=97 r=range L='<' P='+' l=[3933,P,0,1,n,L,2,n,n,P,0,n,3,P,1,n,4] a=lambda i,j:[P,i,j,i] b=lambda i:[P,i,i,i+1] def d(x,i,j): return sum([sum([b(j+t-1),a(j+t,n),*(b(s)for s in r(j+t,j+29)),[L,j+29,x,i+t],b(j+t-1),a(j+t,i+t)],[])for t in r(30)],[]) l+=d(3,5,36) l+=d(4,36,67) for t in r(59): l+=a(2,2) for s in r(t+1): if t-30<s<30:l+=[P,5+t-s,36+s,98];l+=[L,n,98,99];l+=a(2,99) print(*l) ```
output
1
106,774
5
213,549
Provide a correct Python 3 solution for this coding contest problem. This is an output-only problem. You shouldn't read anything from the input. In short, your task is to simulate multiplication by using only comparison (x < y) and addition (x + y). There is no input in this problem, you just print a sequence of operations. Imagine that there is a big array a[0], a[1], ..., a[N-1] of length N. The first two values are initially two non-negative integers A and B (which are unknown to you), the other elements are zeros. Your goal is to get the product A \cdot B in a[2] at the end. You are allowed operations of two types, with the following format (where 0 \leq i, j, k < N): * `+ i j k` — applies operation a[k] = a[i] + a[j]. * `< i j k` — applies operation a[k] = a[i] < a[j]. That is, if a[i] < a[j] then a[k] becomes 1, otherwise it becomes 0. You can use at most Q operations. Elements of a can't exceed V. Indices (i, j, k) don't have to be distinct. It's allowed to modify any element of the array (including the first two). The actual checker simulates the process for multiple pairs (A, B) within a single test. Each time, the checker chooses values A and B, creates the array a = [A, B, 0, 0, \ldots, 0], applies all your operations and ensures that a[2] = A \cdot B. Constraints * 0 \leq A, B \leq 10^9 * N = Q = 200\,000 * V = 10^{19} = 10\,000\,000\,000\,000\,000\,000 Input The Standard Input is empty. Output In the first line, print the number of operations. Each operation should then be printed in a single line of format `+ i j k` or `< i j k`. Example Input Output
instruction
0
106,775
5
213,550
"Correct Solution: ``` n=97 p=print r=range def a(i,j,k,l=0):p("+<"[l],i,j,k) def b(i):a(i,i,i+1) def d(x,i,j): for t in r(30): b(j+t-1);a(j+t,n,j+t) for s in r(j+t,j+29):b(s) a(j+29,x,i+t,1);b(j+t-1);a(j+t,i+t,j+t) p(3933) a(0,1,n) a(2,n,n,1) a(0,n,3) a(1,n,4) d(3,5,36) d(4,36,67) for t in r(59): a(2,2,2) for s in r(t+1): if t-30<s<30:a(5+t-s,36+s,98);a(n,98,99,1);a(2,99,2) ```
output
1
106,775
5
213,551
Provide a correct Python 3 solution for this coding contest problem. This is an output-only problem. You shouldn't read anything from the input. In short, your task is to simulate multiplication by using only comparison (x < y) and addition (x + y). There is no input in this problem, you just print a sequence of operations. Imagine that there is a big array a[0], a[1], ..., a[N-1] of length N. The first two values are initially two non-negative integers A and B (which are unknown to you), the other elements are zeros. Your goal is to get the product A \cdot B in a[2] at the end. You are allowed operations of two types, with the following format (where 0 \leq i, j, k < N): * `+ i j k` — applies operation a[k] = a[i] + a[j]. * `< i j k` — applies operation a[k] = a[i] < a[j]. That is, if a[i] < a[j] then a[k] becomes 1, otherwise it becomes 0. You can use at most Q operations. Elements of a can't exceed V. Indices (i, j, k) don't have to be distinct. It's allowed to modify any element of the array (including the first two). The actual checker simulates the process for multiple pairs (A, B) within a single test. Each time, the checker chooses values A and B, creates the array a = [A, B, 0, 0, \ldots, 0], applies all your operations and ensures that a[2] = A \cdot B. Constraints * 0 \leq A, B \leq 10^9 * N = Q = 200\,000 * V = 10^{19} = 10\,000\,000\,000\,000\,000\,000 Input The Standard Input is empty. Output In the first line, print the number of operations. Each operation should then be printed in a single line of format `+ i j k` or `< i j k`. Example Input Output
instruction
0
106,776
5
213,552
"Correct Solution: ``` n=97 p=print r=range def c(i,j,k):p('<',i,j,k) def a(i,j,k):p('+',i,j,k) def b(i):a(i,i,i+1) def d(x,i,j): for t in r(30): b(j+t-1) a(j+t,n,j+t) for s in r(j+t,j+29):b(s) c(j+29,x,i+t) b(j+t-1) a(j+t,i+t,j+t) p(3933) a(0,1,n) c(2,n,n) a(0,n,3) a(1,n,4) d(3,5,36) d(4,36,67) for t in r(59): a(2,2,2) for s in r(t+1): if t-30<s<30:a(5+t-s,36+s,98);c(n,98,99);a(2,99,2) ```
output
1
106,776
5
213,553
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an output-only problem. You shouldn't read anything from the input. In short, your task is to simulate multiplication by using only comparison (x < y) and addition (x + y). There is no input in this problem, you just print a sequence of operations. Imagine that there is a big array a[0], a[1], ..., a[N-1] of length N. The first two values are initially two non-negative integers A and B (which are unknown to you), the other elements are zeros. Your goal is to get the product A \cdot B in a[2] at the end. You are allowed operations of two types, with the following format (where 0 \leq i, j, k < N): * `+ i j k` — applies operation a[k] = a[i] + a[j]. * `< i j k` — applies operation a[k] = a[i] < a[j]. That is, if a[i] < a[j] then a[k] becomes 1, otherwise it becomes 0. You can use at most Q operations. Elements of a can't exceed V. Indices (i, j, k) don't have to be distinct. It's allowed to modify any element of the array (including the first two). The actual checker simulates the process for multiple pairs (A, B) within a single test. Each time, the checker chooses values A and B, creates the array a = [A, B, 0, 0, \ldots, 0], applies all your operations and ensures that a[2] = A \cdot B. Constraints * 0 \leq A, B \leq 10^9 * N = Q = 200\,000 * V = 10^{19} = 10\,000\,000\,000\,000\,000\,000 Input The Standard Input is empty. Output In the first line, print the number of operations. Each operation should then be printed in a single line of format `+ i j k` or `< i j k`. Example Input Output Submitted Solution: ``` n=97 p=print r=range def c(i,j,k):p('<',i,j,k) def a(i,j,k):p('+',i,j,k) def d(x,i,j): for t in r(30): a(j+t-1,j+t-1,j+t) a(j+t,n,j+t) for s in r(j+t,j+29):a(s,s,s+1) c(j+29,x,i+t) a(j+t-1,j+t-1,j+t) a(j+t,i+t,j+t) p(3933) a(0,1,n) c(2,n,n) a(0,n,3) a(1,n,4) d(3,5,36) d(4,36,67) for t in r(59): a(2,2,2) for s in r(t+1): if t-30<s<30:a(5+t-s,36+s,98);c(n,98,99);a(2,99,2) ```
instruction
0
106,777
5
213,554
Yes
output
1
106,777
5
213,555
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an output-only problem. You shouldn't read anything from the input. In short, your task is to simulate multiplication by using only comparison (x < y) and addition (x + y). There is no input in this problem, you just print a sequence of operations. Imagine that there is a big array a[0], a[1], ..., a[N-1] of length N. The first two values are initially two non-negative integers A and B (which are unknown to you), the other elements are zeros. Your goal is to get the product A \cdot B in a[2] at the end. You are allowed operations of two types, with the following format (where 0 \leq i, j, k < N): * `+ i j k` — applies operation a[k] = a[i] + a[j]. * `< i j k` — applies operation a[k] = a[i] < a[j]. That is, if a[i] < a[j] then a[k] becomes 1, otherwise it becomes 0. You can use at most Q operations. Elements of a can't exceed V. Indices (i, j, k) don't have to be distinct. It's allowed to modify any element of the array (including the first two). The actual checker simulates the process for multiple pairs (A, B) within a single test. Each time, the checker chooses values A and B, creates the array a = [A, B, 0, 0, \ldots, 0], applies all your operations and ensures that a[2] = A \cdot B. Constraints * 0 \leq A, B \leq 10^9 * N = Q = 200\,000 * V = 10^{19} = 10\,000\,000\,000\,000\,000\,000 Input The Standard Input is empty. Output In the first line, print the number of operations. Each operation should then be printed in a single line of format `+ i j k` or `< i j k`. Example Input Output Submitted Solution: ``` n=97 p=print r=range def a(i,j,k,l=0):p("+<"[l],i,j,k) def b(i):a(i,i,i+1) def d(x,i,j): for t in r(30):b(j+t-1);a(j+t,n,j+t);[b(s)for s in r(j+t,j+29)];a(j+29,x,i+t,1);b(j+t-1);a(j+t,i+t,j+t) p(3933) a(0,1,n) a(2,n,n,1) a(0,n,3) a(1,n,4) d(3,5,36) d(4,36,67) for t in r(59):a(2,2,2);[(a(5+t-s,36+s,98),a(n,98,99,1),a(2,99,2))for s in r(t+1)if t-30<s<30] ```
instruction
0
106,778
5
213,556
Yes
output
1
106,778
5
213,557
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an output-only problem. You shouldn't read anything from the input. In short, your task is to simulate multiplication by using only comparison (x < y) and addition (x + y). There is no input in this problem, you just print a sequence of operations. Imagine that there is a big array a[0], a[1], ..., a[N-1] of length N. The first two values are initially two non-negative integers A and B (which are unknown to you), the other elements are zeros. Your goal is to get the product A \cdot B in a[2] at the end. You are allowed operations of two types, with the following format (where 0 \leq i, j, k < N): * `+ i j k` — applies operation a[k] = a[i] + a[j]. * `< i j k` — applies operation a[k] = a[i] < a[j]. That is, if a[i] < a[j] then a[k] becomes 1, otherwise it becomes 0. You can use at most Q operations. Elements of a can't exceed V. Indices (i, j, k) don't have to be distinct. It's allowed to modify any element of the array (including the first two). The actual checker simulates the process for multiple pairs (A, B) within a single test. Each time, the checker chooses values A and B, creates the array a = [A, B, 0, 0, \ldots, 0], applies all your operations and ensures that a[2] = A \cdot B. Constraints * 0 \leq A, B \leq 10^9 * N = Q = 200\,000 * V = 10^{19} = 10\,000\,000\,000\,000\,000\,000 Input The Standard Input is empty. Output In the first line, print the number of operations. Each operation should then be printed in a single line of format `+ i j k` or `< i j k`. Example Input Output Submitted Solution: ``` n=97 def c(i,j,k):print('<',i,j,k) def a(i,j,k):print('+',i,j,k) def m(i,j,k): for t in range(59): a(k,k,k) for s in range(t+1): if t-30<s<30:a(i+t-s,j+s,98);c(n,98,99);a(k,99,k) def d(x,i,j): for t in range(30): a(j+t-1,j+t-1,j+t) a(j+t,n,j+t) for s in range(j+t,j+29):a(s,s,s+1) c(j+29,x,i+t) a(j+t-1,j+t-1,j+t) a(j+t,i+t,j+t) print(3933) a(0,1,n) c(2,n,n) a(0,n,3) a(1,n,4) d(3,5,36) d(4,36,67) for t in range(59): a(2,2,2) for s in range(t+1): if t-30<s<30:a(5+t-s,36+s,98);c(n,98,99);a(2,99,2) ```
instruction
0
106,779
5
213,558
Yes
output
1
106,779
5
213,559
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an output-only problem. You shouldn't read anything from the input. In short, your task is to simulate multiplication by using only comparison (x < y) and addition (x + y). There is no input in this problem, you just print a sequence of operations. Imagine that there is a big array a[0], a[1], ..., a[N-1] of length N. The first two values are initially two non-negative integers A and B (which are unknown to you), the other elements are zeros. Your goal is to get the product A \cdot B in a[2] at the end. You are allowed operations of two types, with the following format (where 0 \leq i, j, k < N): * `+ i j k` — applies operation a[k] = a[i] + a[j]. * `< i j k` — applies operation a[k] = a[i] < a[j]. That is, if a[i] < a[j] then a[k] becomes 1, otherwise it becomes 0. You can use at most Q operations. Elements of a can't exceed V. Indices (i, j, k) don't have to be distinct. It's allowed to modify any element of the array (including the first two). The actual checker simulates the process for multiple pairs (A, B) within a single test. Each time, the checker chooses values A and B, creates the array a = [A, B, 0, 0, \ldots, 0], applies all your operations and ensures that a[2] = A \cdot B. Constraints * 0 \leq A, B \leq 10^9 * N = Q = 200\,000 * V = 10^{19} = 10\,000\,000\,000\,000\,000\,000 Input The Standard Input is empty. Output In the first line, print the number of operations. Each operation should then be printed in a single line of format `+ i j k` or `< i j k`. Example Input Output Submitted Solution: ``` class CodeGen: codes = [] cnt = 100 def __init__(self, A, B): self.A = A self.B = B self.C1 = self.one() self.C2 = self.pow2(self.C1, 1) self.C3 = self.pow2(self.C1, 2) self.C4 = self.pow2(self.C1, 3) self.POW2 = [self.C1] for i in range(32): self.POW2.append(self.pow2(self.C1, i + 1)) def allocate(self): self.cnt += 1 return self.cnt - 1 def plus(self, x, y): l = self.allocate() self.codes.append(f"+ {x} {y} {l}") return l def gt(self, x, y): l = self.allocate() self.codes.append(f"< {x} {y} {l}") return l def ge(self, x, y): return self.gt(x, self.plus(y, self.C1)) def pow2(self, x, n): t = x for _ in range(n): t = self.plus(t, t) return t def one(self): return self.gt(self.allocate(), self.plus(self.A, self.B)) def bits(self, x, n): result = [] t = self.allocate() for i in range(n - 1, -1, -1): bit = self.ge(self.plus(self.POW2[i], t), x) result.append(bit) t = self.plus(t, self.pow2(bit, i)) return result def mult(self, x, y): return self.gt(self.C1, self.plus(x, y)) def show(self, ans): t = self.allocate() self.codes.append(f"+ {ans} {t} 2") print(len(self.codes)) for c in self.codes: print(c) def pluss(self, xs): if len(xs) == 1: return xs[0] return self.plus(xs[0], self.pluss(xs[1:])) class Eval(CodeGen): def __init__(self, A, B): super().__init__(A, B) def allocate(self): return 0 def plus(self, x, y): return x + y def gt(self, x, y): if x < y: return 1 return 0 def show(self, ans): print(ans) if __name__ == "__main__": gen = CodeGen(0, 1) # gen = Eval(1000, 1234) A = gen.bits(gen.A, 32) B = gen.bits(gen.B, 32) X = [] for _ in range(64): X.append(gen.allocate()) for i in range(32): for j in range(32): X[i + j] = gen.plus(X[i + j], gen.mult(A[i], B[j])) ans = gen.allocate() for i in range(64): ans = gen.plus(ans, gen.pow2(X[i], 62- i)) gen.show(ans) ```
instruction
0
106,780
5
213,560
Yes
output
1
106,780
5
213,561
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an output-only problem. You shouldn't read anything from the input. In short, your task is to simulate multiplication by using only comparison (x < y) and addition (x + y). There is no input in this problem, you just print a sequence of operations. Imagine that there is a big array a[0], a[1], ..., a[N-1] of length N. The first two values are initially two non-negative integers A and B (which are unknown to you), the other elements are zeros. Your goal is to get the product A \cdot B in a[2] at the end. You are allowed operations of two types, with the following format (where 0 \leq i, j, k < N): * `+ i j k` — applies operation a[k] = a[i] + a[j]. * `< i j k` — applies operation a[k] = a[i] < a[j]. That is, if a[i] < a[j] then a[k] becomes 1, otherwise it becomes 0. You can use at most Q operations. Elements of a can't exceed V. Indices (i, j, k) don't have to be distinct. It's allowed to modify any element of the array (including the first two). The actual checker simulates the process for multiple pairs (A, B) within a single test. Each time, the checker chooses values A and B, creates the array a = [A, B, 0, 0, \ldots, 0], applies all your operations and ensures that a[2] = A \cdot B. Constraints * 0 \leq A, B \leq 10^9 * N = Q = 200\,000 * V = 10^{19} = 10\,000\,000\,000\,000\,000\,000 Input The Standard Input is empty. Output In the first line, print the number of operations. Each operation should then be printed in a single line of format `+ i j k` or `< i j k`. Example Input Output Submitted Solution: ``` #B=[0 for _ in range(140)] #B[0],B[1] = 0,10 print(245) def f(s): print(s) f('< 2 0 3') for i in range(11): f(f'< 4 0 {5+i}') f(f'+ 3 4 4') for i in range(11): f(f'< 1 16 {17+i}') f(f'+ 3 16 16') for i in range(10): for j in range(10): f(f'< {j+18} {i+5} {28 + 10*i+j}') for i in range(28,28+10*9+9+1): f(f'+ 2 {i} 2') ```
instruction
0
106,781
5
213,562
No
output
1
106,781
5
213,563
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an output-only problem. You shouldn't read anything from the input. In short, your task is to simulate multiplication by using only comparison (x < y) and addition (x + y). There is no input in this problem, you just print a sequence of operations. Imagine that there is a big array a[0], a[1], ..., a[N-1] of length N. The first two values are initially two non-negative integers A and B (which are unknown to you), the other elements are zeros. Your goal is to get the product A \cdot B in a[2] at the end. You are allowed operations of two types, with the following format (where 0 \leq i, j, k < N): * `+ i j k` — applies operation a[k] = a[i] + a[j]. * `< i j k` — applies operation a[k] = a[i] < a[j]. That is, if a[i] < a[j] then a[k] becomes 1, otherwise it becomes 0. You can use at most Q operations. Elements of a can't exceed V. Indices (i, j, k) don't have to be distinct. It's allowed to modify any element of the array (including the first two). The actual checker simulates the process for multiple pairs (A, B) within a single test. Each time, the checker chooses values A and B, creates the array a = [A, B, 0, 0, \ldots, 0], applies all your operations and ensures that a[2] = A \cdot B. Constraints * 0 \leq A, B \leq 10^9 * N = Q = 200\,000 * V = 10^{19} = 10\,000\,000\,000\,000\,000\,000 Input The Standard Input is empty. Output In the first line, print the number of operations. Each operation should then be printed in a single line of format `+ i j k` or `< i j k`. Example Input Output Submitted Solution: ``` ''' 自宅用PCでの解答 ''' import math #import numpy as np import itertools import queue import bisect from collections import deque,defaultdict import heapq as hpq from sys import stdin,setrecursionlimit #from scipy.sparse.csgraph import dijkstra #from scipy.sparse import csr_matrix ipt = stdin.readline setrecursionlimit(10**7) mod = 10**9+7 dir = [(-1,0),(0,-1),(1,0),(0,1)] alp = "abcdefghijklmnopqrstuvwxyz" def main(): print(511) a = [6,9]+[0]*10001 print("+ 0 1 3") a[3] = a[0]+a[1] print("< 2 3 4") a[4] = a[2] < a[3] print("+ 10000 10000 3") a[3] = a[10000]+a[10000] for i in range(8): print("+ 4", i+4, i+5) a[i+5] = a[4]+a[i+4] # print(a) for i in range(10): for j in range(10): print("<", 3+i, 0, 20) print("<", 3+j, 1, 21) print("+", 20, 21, 22) print("<", 4, 22, 23) print("+ 2", 23, 2) a[20] = a[3+i]<a[0] a[21] = a[3+j]<a[1] a[22] = a[20]+a[21] a[23] = a[4]<a[22] a[2] = a[23]+a[2] # print(a[2]) return None if __name__ == '__main__': main() ```
instruction
0
106,782
5
213,564
No
output
1
106,782
5
213,565
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an output-only problem. You shouldn't read anything from the input. In short, your task is to simulate multiplication by using only comparison (x < y) and addition (x + y). There is no input in this problem, you just print a sequence of operations. Imagine that there is a big array a[0], a[1], ..., a[N-1] of length N. The first two values are initially two non-negative integers A and B (which are unknown to you), the other elements are zeros. Your goal is to get the product A \cdot B in a[2] at the end. You are allowed operations of two types, with the following format (where 0 \leq i, j, k < N): * `+ i j k` — applies operation a[k] = a[i] + a[j]. * `< i j k` — applies operation a[k] = a[i] < a[j]. That is, if a[i] < a[j] then a[k] becomes 1, otherwise it becomes 0. You can use at most Q operations. Elements of a can't exceed V. Indices (i, j, k) don't have to be distinct. It's allowed to modify any element of the array (including the first two). The actual checker simulates the process for multiple pairs (A, B) within a single test. Each time, the checker chooses values A and B, creates the array a = [A, B, 0, 0, \ldots, 0], applies all your operations and ensures that a[2] = A \cdot B. Constraints * 0 \leq A, B \leq 10^9 * N = Q = 200\,000 * V = 10^{19} = 10\,000\,000\,000\,000\,000\,000 Input The Standard Input is empty. Output In the first line, print the number of operations. Each operation should then be printed in a single line of format `+ i j k` or `< i j k`. Example Input Output Submitted Solution: ``` P,L="+<" p,r=print,range p(6484,P,0,1,3,L,2,3,3) for x in 0,1:p(P,x,3,x);[[P,v:=x+4,v,v,P,v,3,6,*[P,6,6,6]*(29-t),L,6,x,T:=x*60+9+t,P,v,T,v]for t in r(30)] for t in r(60):p(P,2,2,2);[p(P,8+t-s,69+s,5,L,3,5,6,P,2,6,2)for s in r(t)] ```
instruction
0
106,783
5
213,566
No
output
1
106,783
5
213,567
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an output-only problem. You shouldn't read anything from the input. In short, your task is to simulate multiplication by using only comparison (x < y) and addition (x + y). There is no input in this problem, you just print a sequence of operations. Imagine that there is a big array a[0], a[1], ..., a[N-1] of length N. The first two values are initially two non-negative integers A and B (which are unknown to you), the other elements are zeros. Your goal is to get the product A \cdot B in a[2] at the end. You are allowed operations of two types, with the following format (where 0 \leq i, j, k < N): * `+ i j k` — applies operation a[k] = a[i] + a[j]. * `< i j k` — applies operation a[k] = a[i] < a[j]. That is, if a[i] < a[j] then a[k] becomes 1, otherwise it becomes 0. You can use at most Q operations. Elements of a can't exceed V. Indices (i, j, k) don't have to be distinct. It's allowed to modify any element of the array (including the first two). The actual checker simulates the process for multiple pairs (A, B) within a single test. Each time, the checker chooses values A and B, creates the array a = [A, B, 0, 0, \ldots, 0], applies all your operations and ensures that a[2] = A \cdot B. Constraints * 0 \leq A, B \leq 10^9 * N = Q = 200\,000 * V = 10^{19} = 10\,000\,000\,000\,000\,000\,000 Input The Standard Input is empty. Output In the first line, print the number of operations. Each operation should then be printed in a single line of format `+ i j k` or `< i j k`. Example Input Output Submitted Solution: ``` print("""232 < 2 0 2 < 3 0 3 + 2 3 4 + 2 4 5 + 2 5 6 + 2 6 7 + 2 7 8 + 2 8 9 + 2 9 10 + 2 10 11 + 2 11 12 < 2 0 13 < 3 0 14 < 4 0 15 < 5 0 16 < 6 0 17 < 7 0 18 < 8 0 19 < 9 0 20 < 10 0 21 < 11 0 22 < 1 3 23 < 1 4 24 < 1 5 25 < 1 6 26 < 1 7 27 < 1 8 28 < 1 9 29 < 1 10 30 < 1 11 31 < 1 12 32 < 23 13 101 < 24 13 102 < 25 13 103 < 26 13 104 < 27 13 105 < 28 13 106 < 29 13 107 < 30 13 108 < 31 13 109 < 32 13 110 < 23 14 111 < 24 14 112 < 25 14 113 < 26 14 114 < 27 14 115 < 28 14 116 < 29 14 117 < 30 14 118 < 31 14 119 < 32 14 120 < 23 15 121 < 24 15 122 < 25 15 123 < 26 15 124 < 27 15 125 < 28 15 126 < 29 15 127 < 30 15 128 < 31 15 129 < 32 15 130 < 23 16 131 < 24 16 132 < 25 16 133 < 26 16 134 < 27 16 135 < 28 16 136 < 29 16 137 < 30 16 138 < 31 16 139 < 32 16 140 < 23 17 141 < 24 17 142 < 25 17 143 < 26 17 144 < 27 17 145 < 28 17 146 < 29 17 147 < 30 17 148 < 31 17 149 < 32 17 150 < 23 18 151 < 24 18 152 < 25 18 153 < 26 18 154 < 27 18 155 < 28 18 156 < 29 18 157 < 30 18 158 < 31 18 159 < 32 18 160 < 23 19 161 < 24 19 162 < 25 19 163 < 26 19 164 < 27 19 165 < 28 19 166 < 29 19 167 < 30 19 168 < 31 19 169 < 32 19 170 < 23 20 171 < 24 20 172 < 25 20 173 < 26 20 174 < 27 20 175 < 28 20 176 < 29 20 177 < 30 20 178 < 31 20 179 < 32 20 180 < 23 21 181 < 24 21 182 < 25 21 183 < 26 21 184 < 27 21 185 < 28 21 186 < 29 21 187 < 30 21 188 < 31 21 189 < 32 21 190 < 23 22 191 < 24 22 192 < 25 22 193 < 26 22 194 < 27 22 195 < 28 22 196 < 29 22 197 < 30 22 198 < 31 22 199 < 32 22 200 + 101 233 233 + 102 233 233 + 103 233 233 + 104 233 233 + 105 233 233 + 106 233 233 + 107 233 233 + 108 233 233 + 109 233 233 + 110 233 233 + 111 233 233 + 112 233 233 + 113 233 233 + 114 233 233 + 115 233 233 + 116 233 233 + 117 233 233 + 118 233 233 + 119 233 233 + 120 233 233 + 121 233 233 + 122 233 233 + 123 233 233 + 124 233 233 + 125 233 233 + 126 233 233 + 127 233 233 + 128 233 233 + 129 233 233 + 130 233 233 + 131 233 233 + 132 233 233 + 133 233 233 + 134 233 233 + 135 233 233 + 136 233 233 + 137 233 233 + 138 233 233 + 139 233 233 + 140 233 233 + 141 233 233 + 142 233 233 + 143 233 233 + 144 233 233 + 145 233 233 + 146 233 233 + 147 233 233 + 148 233 233 + 149 233 233 + 150 233 233 + 151 233 233 + 152 233 233 + 153 233 233 + 154 233 233 + 155 233 233 + 156 233 233 + 157 233 233 + 158 233 233 + 159 233 233 + 160 233 233 + 161 233 233 + 162 233 233 + 163 233 233 + 164 233 233 + 165 233 233 + 166 233 233 + 167 233 233 + 168 233 233 + 169 233 233 + 170 233 233 + 171 233 233 + 172 233 233 + 173 233 233 + 174 233 233 + 175 233 233 + 176 233 233 + 177 233 233 + 178 233 233 + 179 233 233 + 180 233 233 + 181 233 233 + 182 233 233 + 183 233 233 + 184 233 233 + 185 233 233 + 186 233 233 + 187 233 233 + 188 233 233 + 189 233 233 + 190 233 233 + 191 233 233 + 192 233 233 + 193 233 233 + 194 233 233 + 195 233 233 + 196 233 233 + 197 233 233 + 198 233 233 + 199 233 233 + 200 233 233 + 233 234 2"""); ```
instruction
0
106,784
5
213,568
No
output
1
106,784
5
213,569
Provide a correct Python 3 solution for this coding contest problem. Example Input 3 0 2 7 2 0 4 5 8 0 Output 11
instruction
0
106,975
5
213,950
"Correct Solution: ``` n = int(input()) graph = [[0 for i in range(n)] for i in range(n)] for i in range(n): graph[i] = list(map(int, input().split())) ans = 0 for i in range(n): for j in range(i+1, n): ans += min(graph[i][j], graph[j][i]) print(ans) ```
output
1
106,975
5
213,951
Provide a correct Python 3 solution for this coding contest problem. Example Input 3 0 2 7 2 0 4 5 8 0 Output 11
instruction
0
106,977
5
213,954
"Correct Solution: ``` import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools sys.setrecursionlimit(10**7) inf = 10**20 eps = 1.0 / 10**10 mod = 998244353 dd = [(0,-1),(1,0),(0,1),(-1,0)] ddn = [(0,-1),(1,-1),(1,0),(1,1),(0,1),(-1,-1),(-1,0),(-1,1)] def LI(): return [int(x) for x in sys.stdin.readline().split()] def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()] def LF(): return [float(x) for x in sys.stdin.readline().split()] def LS(): return sys.stdin.readline().split() def I(): return int(sys.stdin.readline()) def F(): return float(sys.stdin.readline()) def S(): return input() def pf(s): return print(s, flush=True) def main(): rr = [] while True: n = I() a = [LI() for _ in range(n)] r = 0 for i in range(n): for j in range(i+1,n): r += min(a[i][j], a[j][i]) rr.append(r) break return '\n'.join(map(str, rr)) print(main()) ```
output
1
106,977
5
213,955
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Consider the infinite sequence s of positive integers, created by repeating the following steps: 1. Find the lexicographically smallest triple of positive integers (a, b, c) such that * a ⊕ b ⊕ c = 0, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). * a, b, c are not in s. Here triple of integers (a_1, b_1, c_1) is considered to be lexicographically smaller than triple (a_2, b_2, c_2) if sequence [a_1, b_1, c_1] is lexicographically smaller than sequence [a_2, b_2, c_2]. 2. Append a, b, c to s in this order. 3. Go back to the first step. You have integer n. Find the n-th element of s. You have to answer t independent test cases. A sequence a is lexicographically smaller than a sequence b if in the first position where a and b differ, the sequence a has a smaller element than the corresponding element in b. Input The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases. Each of the next t lines contains a single integer n (1≤ n ≤ 10^{16}) — the position of the element you want to know. Output In each of the t lines, output the answer to the corresponding test case. Example Input 9 1 2 3 4 5 6 7 8 9 Output 1 2 3 4 8 12 5 10 15 Note The first elements of s are 1, 2, 3, 4, 8, 12, 5, 10, 15, ... Submitted Solution: ``` memo=[(0,0,0)] def new_find_pair(n): stack=[] while n>=len(memo): N=n.bit_length()-1 if N%2==0: i=N//2 stack.append((n,1,i)) n-=4**i else: i=N//2 if n>>(2*i)&1==0: #type2 stack.append((n,2,i)) n-=2*4**i else: #type3 stack.append((n,3,i)) n-=3*4**i a,b,c=memo[n] for m,t,i in stack[::-1]: m-=t*4**i if t==1: if m==b: a,b,c=b,c,a elif m==c: a,b,c=c,a,b elif t==2: if m==a: a,b,c=c,a,b elif m==c: a,b,c=b,c,a else: if m==a: a,b,c=b,c,a elif m==b: a,b,c=c,a,b a+=4**i b+=2*4**i c+=3*4**i return (a,b,c) for i in range(1,4**5): memo.append(new_find_pair(i)) def nth_pair(n): tmp=0 for i in range(28): tmp+=4**i if tmp>=n: tmp-=4**i first=(n-tmp-1)+4**i return new_find_pair(first) def nth_seq(n): q=(n-1)//3+1 fst=(n-1)%3 res=nth_pair(q)[fst] return res import sys input=sys.stdin.buffer.readline #n=int(input()) #print(find_pair(n)) #print(nth_pair(n)) Q=int(input()) for _ in range(Q): n=int(input()) #n=int(input()) r=nth_seq(n) print(r) #print(nth_pair(q)[fst]) #print(time.time()-start) ```
instruction
0
107,177
5
214,354
Yes
output
1
107,177
5
214,355
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Consider the infinite sequence s of positive integers, created by repeating the following steps: 1. Find the lexicographically smallest triple of positive integers (a, b, c) such that * a ⊕ b ⊕ c = 0, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). * a, b, c are not in s. Here triple of integers (a_1, b_1, c_1) is considered to be lexicographically smaller than triple (a_2, b_2, c_2) if sequence [a_1, b_1, c_1] is lexicographically smaller than sequence [a_2, b_2, c_2]. 2. Append a, b, c to s in this order. 3. Go back to the first step. You have integer n. Find the n-th element of s. You have to answer t independent test cases. A sequence a is lexicographically smaller than a sequence b if in the first position where a and b differ, the sequence a has a smaller element than the corresponding element in b. Input The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases. Each of the next t lines contains a single integer n (1≤ n ≤ 10^{16}) — the position of the element you want to know. Output In each of the t lines, output the answer to the corresponding test case. Example Input 9 1 2 3 4 5 6 7 8 9 Output 1 2 3 4 8 12 5 10 15 Note The first elements of s are 1, 2, 3, 4, 8, 12, 5, 10, 15, ... Submitted Solution: ``` def find_answer(n): trio_num, trio_place = n // 3, n % 3 digit = 1 while trio_num >= 0: trio_num -= digit digit *= 4 digit //= 4 trio_num += digit t1 = digit + trio_num if trio_place == 0: return t1 t2, t3 = digit*2, digit*3 new_digit = 1 while new_digit < digit: x = t1 % 4 if x == 1: t2 += new_digit * 2 t3 += new_digit * 3 elif x == 2: t2 += new_digit * 3 t3 += new_digit * 1 elif x == 3: t2 += new_digit * 1 t3 += new_digit * 2 t1 //= 4 new_digit *= 4 return t2 if trio_place == 1 else t3 if __name__ == '__main__': n = int(input()) ans = [] for i in range(n): x = int(input()) ans += [find_answer(x-1)] for x in ans: print(x) ```
instruction
0
107,178
5
214,356
Yes
output
1
107,178
5
214,357
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Consider the infinite sequence s of positive integers, created by repeating the following steps: 1. Find the lexicographically smallest triple of positive integers (a, b, c) such that * a ⊕ b ⊕ c = 0, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). * a, b, c are not in s. Here triple of integers (a_1, b_1, c_1) is considered to be lexicographically smaller than triple (a_2, b_2, c_2) if sequence [a_1, b_1, c_1] is lexicographically smaller than sequence [a_2, b_2, c_2]. 2. Append a, b, c to s in this order. 3. Go back to the first step. You have integer n. Find the n-th element of s. You have to answer t independent test cases. A sequence a is lexicographically smaller than a sequence b if in the first position where a and b differ, the sequence a has a smaller element than the corresponding element in b. Input The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases. Each of the next t lines contains a single integer n (1≤ n ≤ 10^{16}) — the position of the element you want to know. Output In each of the t lines, output the answer to the corresponding test case. Example Input 9 1 2 3 4 5 6 7 8 9 Output 1 2 3 4 8 12 5 10 15 Note The first elements of s are 1, 2, 3, 4, 8, 12, 5, 10, 15, ... Submitted Solution: ``` import sys input = sys.stdin.readline import bisect L=[4**i for i in range(30)] def calc(x): fami=bisect.bisect_right(L,x)-1 base=(x-L[fami])//3 cl=x%3 if cl==1: return L[fami]+base else: cl1=L[fami]+base ANS=0 for i in range(30): x=cl1//L[i]%4 if x==1: ANS+=2*L[i] elif x==2: ANS+=3*L[i] elif x==3: ANS+=L[i] if cl==2: return ANS else: return ANS^cl1 t=int(input()) for tests in range(t): print(calc(int(input()))) ```
instruction
0
107,179
5
214,358
Yes
output
1
107,179
5
214,359
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Consider the infinite sequence s of positive integers, created by repeating the following steps: 1. Find the lexicographically smallest triple of positive integers (a, b, c) such that * a ⊕ b ⊕ c = 0, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). * a, b, c are not in s. Here triple of integers (a_1, b_1, c_1) is considered to be lexicographically smaller than triple (a_2, b_2, c_2) if sequence [a_1, b_1, c_1] is lexicographically smaller than sequence [a_2, b_2, c_2]. 2. Append a, b, c to s in this order. 3. Go back to the first step. You have integer n. Find the n-th element of s. You have to answer t independent test cases. A sequence a is lexicographically smaller than a sequence b if in the first position where a and b differ, the sequence a has a smaller element than the corresponding element in b. Input The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases. Each of the next t lines contains a single integer n (1≤ n ≤ 10^{16}) — the position of the element you want to know. Output In each of the t lines, output the answer to the corresponding test case. Example Input 9 1 2 3 4 5 6 7 8 9 Output 1 2 3 4 8 12 5 10 15 Note The first elements of s are 1, 2, 3, 4, 8, 12, 5, 10, 15, ... Submitted Solution: ``` def new_find_pair(n): stack=[] while n: N=n.bit_length()-1 if N%2==0: i=N//2 stack.append((n,1,i)) n-=4**i else: i=N//2 if n>>(2*i)&1==0: #type2 stack.append((n,2,i)) n-=2*4**i else: #type3 stack.append((n,3,i)) n-=3*4**i a,b,c=0,0,0 for m,t,i in stack[::-1]: m-=t*4**i if t==1: if m==b: a,b,c=b,c,a elif m==c: a,b,c=c,a,b elif t==2: if m==a: a,b,c=c,a,b elif m==c: a,b,c=b,c,a else: if m==a: a,b,c=b,c,a elif m==b: a,b,c=c,a,b a+=4**i b+=2*4**i c+=3*4**i return (a,b,c) def nth_pair(n): tmp=0 for i in range(28): tmp+=4**i if tmp>=n: tmp-=4**i first=(n-tmp-1)+4**i return new_find_pair(first) def nth_seq(n): q=(n-1)//3+1 fst=(n-1)%3 res=nth_pair(q)[fst] return res import sys input=sys.stdin.buffer.readline #n=int(input()) #print(find_pair(n)) #print(nth_pair(n)) Q=int(input()) for _ in range(Q): n=int(input()) #n=int(input()) r=nth_seq(n) print(r) #print(nth_pair(q)[fst]) #print(time.time()-start) ```
instruction
0
107,180
5
214,360
Yes
output
1
107,180
5
214,361
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Consider the infinite sequence s of positive integers, created by repeating the following steps: 1. Find the lexicographically smallest triple of positive integers (a, b, c) such that * a ⊕ b ⊕ c = 0, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). * a, b, c are not in s. Here triple of integers (a_1, b_1, c_1) is considered to be lexicographically smaller than triple (a_2, b_2, c_2) if sequence [a_1, b_1, c_1] is lexicographically smaller than sequence [a_2, b_2, c_2]. 2. Append a, b, c to s in this order. 3. Go back to the first step. You have integer n. Find the n-th element of s. You have to answer t independent test cases. A sequence a is lexicographically smaller than a sequence b if in the first position where a and b differ, the sequence a has a smaller element than the corresponding element in b. Input The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases. Each of the next t lines contains a single integer n (1≤ n ≤ 10^{16}) — the position of the element you want to know. Output In each of the t lines, output the answer to the corresponding test case. Example Input 9 1 2 3 4 5 6 7 8 9 Output 1 2 3 4 8 12 5 10 15 Note The first elements of s are 1, 2, 3, 4, 8, 12, 5, 10, 15, ... Submitted Solution: ``` def find_answer(n): trio_num, trio_place = n // 3, n % 3 digit = 1 while trio_num >= 0: trio_num -= digit digit *= 4 digit //= 4 trio_num += digit t1 = digit + trio_num if trio_place == 0: return t1 t2, t3 = digit*2, digit*3 new_digit = 1 while new_digit < digit: x = t1 % 4 if x == 1: t2 += new_digit * 2 t3 += new_digit * 3 elif x == 2: t2 += new_digit * 3 t3 += new_digit * 1 elif x == 3: t2 += new_digit * 1 t3 += new_digit * 2 t1 //= 4*new_digit new_digit *= 4 return t2 if trio_place == 1 else t3 if __name__ == '__main__': n = int(input()) ans = [] for i in range(n): x = int(input()) ans += [find_answer(x-1)] for x in ans: print(x) ```
instruction
0
107,181
5
214,362
No
output
1
107,181
5
214,363
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Consider the infinite sequence s of positive integers, created by repeating the following steps: 1. Find the lexicographically smallest triple of positive integers (a, b, c) such that * a ⊕ b ⊕ c = 0, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). * a, b, c are not in s. Here triple of integers (a_1, b_1, c_1) is considered to be lexicographically smaller than triple (a_2, b_2, c_2) if sequence [a_1, b_1, c_1] is lexicographically smaller than sequence [a_2, b_2, c_2]. 2. Append a, b, c to s in this order. 3. Go back to the first step. You have integer n. Find the n-th element of s. You have to answer t independent test cases. A sequence a is lexicographically smaller than a sequence b if in the first position where a and b differ, the sequence a has a smaller element than the corresponding element in b. Input The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases. Each of the next t lines contains a single integer n (1≤ n ≤ 10^{16}) — the position of the element you want to know. Output In each of the t lines, output the answer to the corresponding test case. Example Input 9 1 2 3 4 5 6 7 8 9 Output 1 2 3 4 8 12 5 10 15 Note The first elements of s are 1, 2, 3, 4, 8, 12, 5, 10, 15, ... Submitted Solution: ``` def find_answer(n): trio_num, trio_place = n // 3, n % 3 digit = 1 while trio_num >= 0: trio_num -= digit digit *= 4 digit //= 4 trio_num += digit t1 = digit + trio_num if trio_place == 0: return t1 t2, t3 = digit*2, digit*3 new_digit = 1 while new_digit < digit: x = t1 % (4*new_digit) if x == 1: t2 += new_digit * 2 t3 += new_digit * 3 elif x == 2: t2 += new_digit * 3 t3 += new_digit * 1 elif x == 3: t2 += new_digit * 1 t3 += new_digit * 2 t1 -= x * new_digit new_digit *= 4 return t2 if trio_place == 1 else t3 if __name__ == '__main__': '''n = int(input()) ans = [] for i in range(n): x = int(input()) ans += [find_answer(x-1)] for x in ans: print(x)''' for x in range(1, 20): print(find_answer(x-1)) ```
instruction
0
107,182
5
214,364
No
output
1
107,182
5
214,365
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Consider the infinite sequence s of positive integers, created by repeating the following steps: 1. Find the lexicographically smallest triple of positive integers (a, b, c) such that * a ⊕ b ⊕ c = 0, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). * a, b, c are not in s. Here triple of integers (a_1, b_1, c_1) is considered to be lexicographically smaller than triple (a_2, b_2, c_2) if sequence [a_1, b_1, c_1] is lexicographically smaller than sequence [a_2, b_2, c_2]. 2. Append a, b, c to s in this order. 3. Go back to the first step. You have integer n. Find the n-th element of s. You have to answer t independent test cases. A sequence a is lexicographically smaller than a sequence b if in the first position where a and b differ, the sequence a has a smaller element than the corresponding element in b. Input The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases. Each of the next t lines contains a single integer n (1≤ n ≤ 10^{16}) — the position of the element you want to know. Output In each of the t lines, output the answer to the corresponding test case. Example Input 9 1 2 3 4 5 6 7 8 9 Output 1 2 3 4 8 12 5 10 15 Note The first elements of s are 1, 2, 3, 4, 8, 12, 5, 10, 15, ... Submitted Solution: ``` def find_answer(n): trio_num, trio_place = n // 3, n % 3 digit = 1 while trio_num >= 0: trio_num -= digit digit *= 4 digit //= 4 trio_num += digit t1 = digit + trio_num if trio_place == 0: return t1 t2, t3 = digit*2, digit*3 new_digit = 1 while new_digit < digit: x = t1 % (4*new_digit) if x == 1: t2 += new_digit * 2 t3 += new_digit * 3 elif x == 2: t2 += new_digit * 3 t3 += new_digit * 1 elif x == 3: t2 += new_digit * 1 t3 += new_digit * 2 t1 -= x * new_digit new_digit *= 4 return t2 if trio_place == 1 else t3 if __name__ == '__main__': n = int(input()) ans = [] for i in range(n): x = int(input()) ans += [find_answer(x-1)] for x in ans: print(x) ```
instruction
0
107,183
5
214,366
No
output
1
107,183
5
214,367
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Consider the infinite sequence s of positive integers, created by repeating the following steps: 1. Find the lexicographically smallest triple of positive integers (a, b, c) such that * a ⊕ b ⊕ c = 0, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). * a, b, c are not in s. Here triple of integers (a_1, b_1, c_1) is considered to be lexicographically smaller than triple (a_2, b_2, c_2) if sequence [a_1, b_1, c_1] is lexicographically smaller than sequence [a_2, b_2, c_2]. 2. Append a, b, c to s in this order. 3. Go back to the first step. You have integer n. Find the n-th element of s. You have to answer t independent test cases. A sequence a is lexicographically smaller than a sequence b if in the first position where a and b differ, the sequence a has a smaller element than the corresponding element in b. Input The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases. Each of the next t lines contains a single integer n (1≤ n ≤ 10^{16}) — the position of the element you want to know. Output In each of the t lines, output the answer to the corresponding test case. Example Input 9 1 2 3 4 5 6 7 8 9 Output 1 2 3 4 8 12 5 10 15 Note The first elements of s are 1, 2, 3, 4, 8, 12, 5, 10, 15, ... Submitted Solution: ``` #!/usr/bin/env python3 import sys input = sys.stdin.readline from itertools import combinations t = int(input()) for tt in range(t): n = int(input()) - 1 mod3 = n % 3 n = n // 3 i = 0 while n >= 4**i: n -= 4**i i += 1 if i == 0: a = 1; b = 2; c = 3 else: a = 4**i + n left = 0 right = 4**i b = 4**i * 2 t = n while right - left > 1: mid1 = (left * 3 + right) // 4 mid2 = (left * 2 + right * 2) // 4 mid3 = (left + right * 3) // 4 rng = right - left if left <= t < mid1: right = mid1 b += 0 elif mid1 <= t < mid2: left = mid1 right = mid2 b += rng // 4 * 2 elif mid2 <= t < mid3: left = mid2 right = mid3 b += rng // 4 * 3 else: left = mid3 b += rng // 4 * 1 t %= rng // 4 c = a ^ b # print("#", tt + 1) if mod3 == 0: print(a) elif mod3 == 1: print(b) else: print(c) # not_used = set([item for item in range(1, 200)]) # for i in range(25): # li = list(not_used) # li.sort() # for comb in combinations(li, 3): # if comb[0] ^ comb[1] ^ comb[2] == 0: # print(comb) # not_used.remove(comb[0]) # not_used.remove(comb[1]) # not_used.remove(comb[2]) # break ```
instruction
0
107,184
5
214,368
No
output
1
107,184
5
214,369
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Anton goes to school, his favorite lessons are arraystudying. He usually solves all the tasks pretty fast, but this time the teacher gave him a complicated one: given two arrays b and c of length n, find array a, such that: <image> where a and b means bitwise AND, while a or b means bitwise OR. Usually Anton is good in arraystudying, but this problem is too hard, so Anton asks you to help. Input The first line of the input contains a single integers n (1 ≤ n ≤ 200 000) — the size of arrays b and c. The second line contains n integers bi (0 ≤ bi ≤ 109) — elements of the array b. Third line contains n integers ci (0 ≤ ci ≤ 109) — elements of the array c. Output If there is no solution, print - 1. Otherwise, the only line of the output should contain n non-negative integers ai — elements of the array a. If there are multiple possible solutions, you may print any of them. Examples Input 4 6 8 4 4 16 22 10 10 Output 3 5 1 1 Input 5 8 25 14 7 16 19 6 9 4 25 Output -1 Submitted Solution: ``` n = int(input()) b = list(map(int, input().split())) c = list(map(int, input().split())) a = [0]*n def fun(): sumb,sumc = sum(b),sum(c) if(sumb+sumc)%(2*n): return False suma = (sumb+sumc)//(2*n) for i in range(n): tmp = (c[i]+b[i]-suma) if c[i]<b[i]: return False if tmp<0: return False if tmp%n: return False a[i] = tmp//n if suma != sum(a): return False if n == 1 and b[0]!=c[0]: return False return True ok = fun() if not ok: print(-1) else: print(' '.join([str(x) for x in a])) ```
instruction
0
107,487
5
214,974
No
output
1
107,487
5
214,975
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Anton goes to school, his favorite lessons are arraystudying. He usually solves all the tasks pretty fast, but this time the teacher gave him a complicated one: given two arrays b and c of length n, find array a, such that: <image> where a and b means bitwise AND, while a or b means bitwise OR. Usually Anton is good in arraystudying, but this problem is too hard, so Anton asks you to help. Input The first line of the input contains a single integers n (1 ≤ n ≤ 200 000) — the size of arrays b and c. The second line contains n integers bi (0 ≤ bi ≤ 109) — elements of the array b. Third line contains n integers ci (0 ≤ ci ≤ 109) — elements of the array c. Output If there is no solution, print - 1. Otherwise, the only line of the output should contain n non-negative integers ai — elements of the array a. If there are multiple possible solutions, you may print any of them. Examples Input 4 6 8 4 4 16 22 10 10 Output 3 5 1 1 Input 5 8 25 14 7 16 19 6 9 4 25 Output -1 Submitted Solution: ``` n = int(input()) a = [int(x) for x in input().split()] b = [int(x) for x in input().split()] sum1 = sum([x+y for x,y in zip(a,b)]) if sum1 %(2*n) != 0 : print(-1) exit() sumAi = sum1 // (2*n) ans = [-1 if (x+y-sumAi) % n != 0 else (x+y-sumAi)//n for x,y in zip(a,b)] if len(list(filter(lambda x : x<0,ans))) != 0 : print(-1) else : print(' '.join(map(str,ans))) ```
instruction
0
107,488
5
214,976
No
output
1
107,488
5
214,977
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Anton goes to school, his favorite lessons are arraystudying. He usually solves all the tasks pretty fast, but this time the teacher gave him a complicated one: given two arrays b and c of length n, find array a, such that: <image> where a and b means bitwise AND, while a or b means bitwise OR. Usually Anton is good in arraystudying, but this problem is too hard, so Anton asks you to help. Input The first line of the input contains a single integers n (1 ≤ n ≤ 200 000) — the size of arrays b and c. The second line contains n integers bi (0 ≤ bi ≤ 109) — elements of the array b. Third line contains n integers ci (0 ≤ ci ≤ 109) — elements of the array c. Output If there is no solution, print - 1. Otherwise, the only line of the output should contain n non-negative integers ai — elements of the array a. If there are multiple possible solutions, you may print any of them. Examples Input 4 6 8 4 4 16 22 10 10 Output 3 5 1 1 Input 5 8 25 14 7 16 19 6 9 4 25 Output -1 Submitted Solution: ``` n,b,c = int(input()), input().split(), input().split() a = [-1 for i in range(n)] for i in range(n): b[i] = int(b[i]) c[i] = int(c[i]) if c[i] < b[i]: print(-1) exit(0) if n==1: if b[0] != c[0]: print(-1) exit(0) else: print(b[0]) exit(0) s1 = sum([b[i] + c[i] for i in range(n)]) if s1 % 2*n != 0: print(-1) exit(0) s1 //= 2*n for i in range(n): x = b[i] + c[i] - s1 if x % n != 0: print(-1) exit(0) else: a[i] = x // n for i in range(n): if i == n-1: end = '\n' else: end = ' ' print(a[i], end = end) ```
instruction
0
107,489
5
214,978
No
output
1
107,489
5
214,979
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Anton goes to school, his favorite lessons are arraystudying. He usually solves all the tasks pretty fast, but this time the teacher gave him a complicated one: given two arrays b and c of length n, find array a, such that: <image> where a and b means bitwise AND, while a or b means bitwise OR. Usually Anton is good in arraystudying, but this problem is too hard, so Anton asks you to help. Input The first line of the input contains a single integers n (1 ≤ n ≤ 200 000) — the size of arrays b and c. The second line contains n integers bi (0 ≤ bi ≤ 109) — elements of the array b. Third line contains n integers ci (0 ≤ ci ≤ 109) — elements of the array c. Output If there is no solution, print - 1. Otherwise, the only line of the output should contain n non-negative integers ai — elements of the array a. If there are multiple possible solutions, you may print any of them. Examples Input 4 6 8 4 4 16 22 10 10 Output 3 5 1 1 Input 5 8 25 14 7 16 19 6 9 4 25 Output -1 Submitted Solution: ``` n=int(input()) b=list(map(int, input().split())) c=list(map(int, input().split())) if n==1: print(b[0] if b==c else -1) exit() s=sum(b+c) if s%(n<<1)!=0: print(-1) exit() s//=(n<<1) a=[b[i]+c[i]-s for i in range(n)] if any(x<0 or x%n!=0 for x in a): print(-1) exit() print(*[x//n for x in a]) ```
instruction
0
107,490
5
214,980
No
output
1
107,490
5
214,981
Provide a correct Python 3 solution for this coding contest problem. There are some animals in a garden. Each of them is a crane with two legs or a turtle with four legs. Takahashi says: "there are X animals in total in the garden, and they have Y legs in total." Determine whether there is a combination of numbers of cranes and turtles in which this statement is correct. Constraints * 1 \leq X \leq 100 * 1 \leq Y \leq 100 * All values in input are integers. Input Input is given from Standard Input in the following format: X Y Output If there is a combination of numbers of cranes and turtles in which the statement is correct, print `Yes`; otherwise, print `No`. Examples Input 3 8 Output Yes Input 2 100 Output No Input 1 2 Output Yes
instruction
0
107,622
5
215,244
"Correct Solution: ``` x,y = map(int, input().split()) print("Yes" if y <= (4*x) and y >= 2*x and y&1!=1 else "No") ```
output
1
107,622
5
215,245
Provide a correct Python 3 solution for this coding contest problem. There are some animals in a garden. Each of them is a crane with two legs or a turtle with four legs. Takahashi says: "there are X animals in total in the garden, and they have Y legs in total." Determine whether there is a combination of numbers of cranes and turtles in which this statement is correct. Constraints * 1 \leq X \leq 100 * 1 \leq Y \leq 100 * All values in input are integers. Input Input is given from Standard Input in the following format: X Y Output If there is a combination of numbers of cranes and turtles in which the statement is correct, print `Yes`; otherwise, print `No`. Examples Input 3 8 Output Yes Input 2 100 Output No Input 1 2 Output Yes
instruction
0
107,623
5
215,246
"Correct Solution: ``` x,y=map(int,input().split()) if y>=2*x and 4*x>=y and y%2==0: print('Yes') else: print('No') ```
output
1
107,623
5
215,247
Provide a correct Python 3 solution for this coding contest problem. There are some animals in a garden. Each of them is a crane with two legs or a turtle with four legs. Takahashi says: "there are X animals in total in the garden, and they have Y legs in total." Determine whether there is a combination of numbers of cranes and turtles in which this statement is correct. Constraints * 1 \leq X \leq 100 * 1 \leq Y \leq 100 * All values in input are integers. Input Input is given from Standard Input in the following format: X Y Output If there is a combination of numbers of cranes and turtles in which the statement is correct, print `Yes`; otherwise, print `No`. Examples Input 3 8 Output Yes Input 2 100 Output No Input 1 2 Output Yes
instruction
0
107,624
5
215,248
"Correct Solution: ``` X, Y = map(int, input().split()) if 2*X <= Y <= 4*X and Y%2 == 0: print('Yes') else: print('No') ```
output
1
107,624
5
215,249
Provide a correct Python 3 solution for this coding contest problem. There are some animals in a garden. Each of them is a crane with two legs or a turtle with four legs. Takahashi says: "there are X animals in total in the garden, and they have Y legs in total." Determine whether there is a combination of numbers of cranes and turtles in which this statement is correct. Constraints * 1 \leq X \leq 100 * 1 \leq Y \leq 100 * All values in input are integers. Input Input is given from Standard Input in the following format: X Y Output If there is a combination of numbers of cranes and turtles in which the statement is correct, print `Yes`; otherwise, print `No`. Examples Input 3 8 Output Yes Input 2 100 Output No Input 1 2 Output Yes
instruction
0
107,626
5
215,252
"Correct Solution: ``` x,y = map(int,input().split()) print('Yes' if x*2 <= y <= x*4 and y % 2 == 0 else 'No') ```
output
1
107,626
5
215,253
Provide a correct Python 3 solution for this coding contest problem. There are some animals in a garden. Each of them is a crane with two legs or a turtle with four legs. Takahashi says: "there are X animals in total in the garden, and they have Y legs in total." Determine whether there is a combination of numbers of cranes and turtles in which this statement is correct. Constraints * 1 \leq X \leq 100 * 1 \leq Y \leq 100 * All values in input are integers. Input Input is given from Standard Input in the following format: X Y Output If there is a combination of numbers of cranes and turtles in which the statement is correct, print `Yes`; otherwise, print `No`. Examples Input 3 8 Output Yes Input 2 100 Output No Input 1 2 Output Yes
instruction
0
107,628
5
215,256
"Correct Solution: ``` x, y = map(int, input().split()) print("Yes" if x*2 <= y <= x*4 and y%2 == 0 else "No") ```
output
1
107,628
5
215,257
Provide a correct Python 3 solution for this coding contest problem. There are some animals in a garden. Each of them is a crane with two legs or a turtle with four legs. Takahashi says: "there are X animals in total in the garden, and they have Y legs in total." Determine whether there is a combination of numbers of cranes and turtles in which this statement is correct. Constraints * 1 \leq X \leq 100 * 1 \leq Y \leq 100 * All values in input are integers. Input Input is given from Standard Input in the following format: X Y Output If there is a combination of numbers of cranes and turtles in which the statement is correct, print `Yes`; otherwise, print `No`. Examples Input 3 8 Output Yes Input 2 100 Output No Input 1 2 Output Yes
instruction
0
107,629
5
215,258
"Correct Solution: ``` x,y=map(int,input().split()) if y%2==0 and y/x<=4 and y/x>=2: print("Yes") else: print("No") ```
output
1
107,629
5
215,259
Provide a correct Python 3 solution for this coding contest problem. We have a sequence of k numbers: d_0,d_1,...,d_{k - 1}. Process the following q queries in order: * The i-th query contains three integers n_i, x_i, and m_i. Let a_0,a_1,...,a_{n_i - 1} be the following sequence of n_i numbers: \begin{eqnarray} a_j = \begin{cases} x_i & ( j = 0 ) \\\ a_{j - 1} + d_{(j - 1)~\textrm{mod}~k} & ( 0 < j \leq n_i - 1 ) \end{cases}\end{eqnarray} Print the number of j~(0 \leq j < n_i - 1) such that (a_j~\textrm{mod}~m_i) < (a_{j + 1}~\textrm{mod}~m_i). Here (y~\textrm{mod}~z) denotes the remainder of y divided by z, for two integers y and z~(z > 0). Constraints * All values in input are integers. * 1 \leq k, q \leq 5000 * 0 \leq d_i \leq 10^9 * 2 \leq n_i \leq 10^9 * 0 \leq x_i \leq 10^9 * 2 \leq m_i \leq 10^9 Input Input is given from Standard Input in the following format: k q d_0 d_1 ... d_{k - 1} n_1 x_1 m_1 n_2 x_2 m_2 : n_q x_q m_q Output Print q lines. The i-th line should contain the response to the i-th query. Examples Input 3 1 3 1 4 5 3 2 Output 1 Input 7 3 27 18 28 18 28 46 1000000000 1000000000 1 7 1000000000 2 10 1000000000 3 12 Output 224489796 214285714 559523809
instruction
0
107,638
5
215,276
"Correct Solution: ``` def i1(): return int(input()) def i2(): return [int(i) for i in input().split()] [k,q]=i2() d=i2() for i in range(q): [n,x,m]=i2() di=[] dz=[] for i in d: di.append(i%m) if i%m==0: dz.append(1) else: dz.append(0) x=((n-1)//k)*sum(di[:k])+x%m if (n-1)%k: x+=sum(di[:(n-1)%k]) ans=n-1-x//m-((n-1)//k)*sum(dz[:k]) if (n-1)%k: ans-=sum(dz[:(n-1)%k]) print(ans) ```
output
1
107,638
5
215,277
Provide a correct Python 3 solution for this coding contest problem. We have a sequence of k numbers: d_0,d_1,...,d_{k - 1}. Process the following q queries in order: * The i-th query contains three integers n_i, x_i, and m_i. Let a_0,a_1,...,a_{n_i - 1} be the following sequence of n_i numbers: \begin{eqnarray} a_j = \begin{cases} x_i & ( j = 0 ) \\\ a_{j - 1} + d_{(j - 1)~\textrm{mod}~k} & ( 0 < j \leq n_i - 1 ) \end{cases}\end{eqnarray} Print the number of j~(0 \leq j < n_i - 1) such that (a_j~\textrm{mod}~m_i) < (a_{j + 1}~\textrm{mod}~m_i). Here (y~\textrm{mod}~z) denotes the remainder of y divided by z, for two integers y and z~(z > 0). Constraints * All values in input are integers. * 1 \leq k, q \leq 5000 * 0 \leq d_i \leq 10^9 * 2 \leq n_i \leq 10^9 * 0 \leq x_i \leq 10^9 * 2 \leq m_i \leq 10^9 Input Input is given from Standard Input in the following format: k q d_0 d_1 ... d_{k - 1} n_1 x_1 m_1 n_2 x_2 m_2 : n_q x_q m_q Output Print q lines. The i-th line should contain the response to the i-th query. Examples Input 3 1 3 1 4 5 3 2 Output 1 Input 7 3 27 18 28 18 28 46 1000000000 1000000000 1 7 1000000000 2 10 1000000000 3 12 Output 224489796 214285714 559523809
instruction
0
107,639
5
215,278
"Correct Solution: ``` K, Q = map(int, input().split()) D = [int(a) for a in input().split()] for _ in range(Q): N, X, M = map(int, input().split()) if N <= K + 1: A = [0] * N A[0] = X % M ans = 0 for i in range(N-1): A[i+1] = (A[i] + D[i]) % M if A[i+1] > A[i]: ans += 1 print(ans) continue ans = N - 1 t = X%M for i in range(K): d = (D[i]-1) % M + 1 a = (N-i-2) // K + 1 t += d * a ans -= t // M print(ans) ```
output
1
107,639
5
215,279
Provide a correct Python 3 solution for this coding contest problem. We have a sequence of k numbers: d_0,d_1,...,d_{k - 1}. Process the following q queries in order: * The i-th query contains three integers n_i, x_i, and m_i. Let a_0,a_1,...,a_{n_i - 1} be the following sequence of n_i numbers: \begin{eqnarray} a_j = \begin{cases} x_i & ( j = 0 ) \\\ a_{j - 1} + d_{(j - 1)~\textrm{mod}~k} & ( 0 < j \leq n_i - 1 ) \end{cases}\end{eqnarray} Print the number of j~(0 \leq j < n_i - 1) such that (a_j~\textrm{mod}~m_i) < (a_{j + 1}~\textrm{mod}~m_i). Here (y~\textrm{mod}~z) denotes the remainder of y divided by z, for two integers y and z~(z > 0). Constraints * All values in input are integers. * 1 \leq k, q \leq 5000 * 0 \leq d_i \leq 10^9 * 2 \leq n_i \leq 10^9 * 0 \leq x_i \leq 10^9 * 2 \leq m_i \leq 10^9 Input Input is given from Standard Input in the following format: k q d_0 d_1 ... d_{k - 1} n_1 x_1 m_1 n_2 x_2 m_2 : n_q x_q m_q Output Print q lines. The i-th line should contain the response to the i-th query. Examples Input 3 1 3 1 4 5 3 2 Output 1 Input 7 3 27 18 28 18 28 46 1000000000 1000000000 1 7 1000000000 2 10 1000000000 3 12 Output 224489796 214285714 559523809
instruction
0
107,640
5
215,280
"Correct Solution: ``` import sys input = sys.stdin.buffer.readline k, q = map(int, (input().split())) d = list(map(int, (input().split()))) for qi in range(q): n, x, m = map(int, input().split()) last = x eq = 0 for i in range(k): num = ((n-1-i)+(k-1))//k last += (d[i]%m) * num if d[i]%m == 0: eq += num ans = (n-1) - (last//m - x//m) - eq print(ans) ```
output
1
107,640
5
215,281
Provide a correct Python 3 solution for this coding contest problem. We have a sequence of k numbers: d_0,d_1,...,d_{k - 1}. Process the following q queries in order: * The i-th query contains three integers n_i, x_i, and m_i. Let a_0,a_1,...,a_{n_i - 1} be the following sequence of n_i numbers: \begin{eqnarray} a_j = \begin{cases} x_i & ( j = 0 ) \\\ a_{j - 1} + d_{(j - 1)~\textrm{mod}~k} & ( 0 < j \leq n_i - 1 ) \end{cases}\end{eqnarray} Print the number of j~(0 \leq j < n_i - 1) such that (a_j~\textrm{mod}~m_i) < (a_{j + 1}~\textrm{mod}~m_i). Here (y~\textrm{mod}~z) denotes the remainder of y divided by z, for two integers y and z~(z > 0). Constraints * All values in input are integers. * 1 \leq k, q \leq 5000 * 0 \leq d_i \leq 10^9 * 2 \leq n_i \leq 10^9 * 0 \leq x_i \leq 10^9 * 2 \leq m_i \leq 10^9 Input Input is given from Standard Input in the following format: k q d_0 d_1 ... d_{k - 1} n_1 x_1 m_1 n_2 x_2 m_2 : n_q x_q m_q Output Print q lines. The i-th line should contain the response to the i-th query. Examples Input 3 1 3 1 4 5 3 2 Output 1 Input 7 3 27 18 28 18 28 46 1000000000 1000000000 1 7 1000000000 2 10 1000000000 3 12 Output 224489796 214285714 559523809
instruction
0
107,641
5
215,282
"Correct Solution: ``` K, Q = map(int, input().split()) *D, = map(int, input().split()) for q in range(Q): n, x, m = map(int, input().split()) r = (n - 1) % K D1r_count0 = 0 D1_count0 = 0 D1_sum = 0 D1r_sum = 0 for k in range(K): if k < r: if D[k] % m == 0: D1r_count0 += 1 D1r_sum += D[k] % m if D[k] % m == 0: D1_count0 += 1 D1_sum += D[k] % m cnt_0 = D1_count0 * ((n - 1) // K) + D1r_count0 a = x # 第n-1項を求める b = a + D1_sum * ((n - 1) // K) + D1r_sum # 繰り上がりの回数 cnt_p = b // m - a // m cnt_n = (n - 1) - cnt_0 - cnt_p print(cnt_n) ```
output
1
107,641
5
215,283